Some very short descriptions (assuming the thrower is right-handed):

For the Backhand

1. Straight throw - this is what I presume you already know. It's most likely the backhand throw you would make for someone 20 yards up ahead to the left when no one is covering you.
2. Airbounce - already discussed on the net. I use it whenever I want the disc to hang a bit, or to make a slow throw. It's good when you are throwing, e.g., to a wide open space and you are expecting your receiver to outrun his/her defender. Just lay it out there and make 'em run to get it.
3. Inside out - that's a throw that goes to the right and curves to the left, because the disc is tilted down to the left more than usual. It's tough to throw it when someone is marking you. Nevertheless, when people are cutting deep from your left to your right, it can be a useful throw (although the reverse curve forehand is probably better for most people).
4. Reverse Curve - a throw that starts to the left and curves to the right. This is a very important throw because when a person is marking you, most backhand throws will be for people cutting from the middle of the field to your left, and you want the throw to curve into them. Also, if there is a defender halfway between you and your receiver, this is the throw that will get it around that defender. The disc is released with much less inward tilt than normal - occasionally even in a position where the right side of the disc is tilted down.
5. High release - this is a short backhand throw that is released flat, but at about top-of-head level. Since most markers keep their hands low, this is a good throw to break the mark if you're throwing short. With a quick release, it is very hard to block.

For the forehand - you have pretty much just the opposite:

1. Straight throw - obvious.
2. Inside-out - the outer edge of the disc is tilted *way* down towards the ground and can be used to throw a forehand to the left side of the field when the marker is trying to force you to the right side of the field.
3. Reverse curve - kinds of the opposite of #2. It curves from the right to the left. It is just as essential, and used for the same reasons, as backhand #4 above.
4. Blade - an extreme verson of the reverse curve - it goes high up in the air and curves slightly to the left. Excellent for throwing around and above defenders, but difficult to control in the wind (esp. a crosswind), and difficult for many to catch.

Others

1. Lift Pass - (I don't really know what you would call this). It's a simple back hand whith a much lower spin to upward lift ratio. Keeping the disc parallel to the ground with a backhand grip, bring it up and release at shoulder level, at the last munute putting a little spin on the disc with a slight flick of the wrist. The flight is path will be parabolic ideally. It's essentially a very short pass with the flight time increased. This is an excellent throw in high wind situations.
2. Scoobie - (aka Scoober, Scooper, or "Keep that in your pocket showboat"). The disc is held just like a hammer and is thrown like one, but it's all wrist, no arm. Good for breaking the force over the right shoulder of your marker. Not good for more than 8-10 yards.
3. Thumber - The inverse of a hammer in terms of flight path. The grip is the tricky part to explain. Extend hand palm up, thumb opposed. Place disc in hand (bottom up) so the dome is resting on your fingers. Rotate the far edge of the disc clockwise until the rim comes to rest upon the side of your thumb. Keep your grip loose when you throw. Arm should be at about a 45 to 50 degree angle. Use more wrist than arm.
4. Squanto - Hold disc upside down with thumb inside rim, release as you would a blade. (settles upside down like overhead. There is an as-yet-unnamed version of this in which the release is more over your head and it flies in a more right-side-up manner, but definitely on a high blade arc.)
5. Falafel - Hold disc with thumb and pinky along outside edge, other three fingers on top (tricky, but can be done... sort of like palming a basketball). Throw in backhand motion. Very mucj like a push-pass.

How to Hold the Disc

The topic of grips is one often overlooked in ultimate, apart from when a new player is first learning. Even if it is noticed, it may be derided, spoken in the same way as many ultimate players say "disc golf". Despite this, very few players actually think about what grip they use for various throws, and even less about why they use a particular grip. This is surprising, as grip plays a significant part in whether a throw is a good one or not.

Backhand Grips

Basic (Beginner's) Grip

Shown are a couple of different versions of this grip. It is characterised by the index finger of the throwing hand being placed along the outside rim of the disc.

The first version has the middle finger of the throwing hand extended towards the centre of the disc. This version gives a high degree of control and stability, since the index finger along the rim helps with direction and the middle finger supporting the disc supplies stability.

On the down side, there are only two fingers gripping the rim, and this leads to much less power than most of the other grips. Most of the power in a grip comes from the ripping of the disc off the end of the index finger.

The second version is one rarely seen. It has the index finger on the rim but not the middle finger support. It gives a little more power as more fingers are gripping the rim, but the power gain is fairly insignificant compared to the loss of control. Bigger power gains are obtained by having the index finger gripping the rim.

 

Power Grip

This is the most popular grip among experienced throwers, and is the one used by almost all disc golfers. All fingers are gripping the rim tightly, and there are no fingers supporting the disc. This means there is a considerable loss of control, since the release point is much harder to judge. A fair degree of control can be regained through practice, and the loss is offset in some ways by the large power gain produced by the disc ripping off the end of the index finger. This grip does however make it harder to throw the high backhand as there is no support for the sharp upward push on the disc just prior to release.

A certain amount of control also depends on the position of the thumb, and how tight the grip is on the disc. In general, the tighter the grip, the more spin which is able to be imparted to the disc, and hence better control in the wind. The thumb can also be placed anywhere from along the rim of the disc to pointing towards the centre of the disc. The best control, particularly with respect to air bounces, is to have the thumb pointing towards the centre of the disc, and this also aids a tight grip. A tight grip also keeps the disc steady and makes high backhands easier to throw. On the down side, it seems a little harder to get as much distance with the thumb pointing toward the middle. This is because of the tendency to drag the thumb across the back edge of the disc on release.

Hybrid Grip

As its name suggests, this grip is a combination of the two grips shown above. It provides power with the index finger gripping the rim. It also gives support in an unusual way. The middle finger of the throwing hand is slightly extended so that the disc is supported by it. This grip makes it possible to throw all throws easily, including high backhands, without the need to change grips. The drawback is a slight loss of power in the throw, in the order of 5m over a 60m throw relative to a power grip. The comments with regard to thumb position apply equally to the hybrid grip as well as the power grip.

Forehand Grips

Basic (Beginner's) Grip

This grip is in principle very similar to the corresponding backhand grip. The middle finger of the throwing hand is inside the rim and the index finger is extended towards the centre of the disc for support. The advantage of this method is control. The disadvantage is a corresponding loss of power, because the spreading of the fingers makes it impossible to cock the wrist back as far just before release.

 

Power Grip

There are a couple of different versions of this grip.

The first has the index finger next to the middle finger and hard up against the rim. This grip increases power since the wrist can now be cocked back further and more snap imparted no the disc. As expected, there is a loss of control as there is no finger to support the disc. The disc has a tendency to wobble up and down, and this can reduce distance if the disc and the wrist are not at the same angle at release.

The second is a slight improvement (not pictured), where the index and middle fingers are slightly curled, and the disc can balance on these two fingers prior to the throw. This grip is more like the hybrid grip below in the way it provides support. It also makes it easier to throw the high forehand.

Like the backhand, the thumb should be used to grip the disc tightly. This will give better spin and more control in the wind, since the disc has less tendency to wobble during the wind-up and throw.

Hybrid Grip

This grip is analogous to the hybrid backhand grip, although it does seem to be more popular and widely used. Instead of the index finger and middle fingers being parallel, the index finger is slightly bent. This is exaggerated a little in the diagram. The pad of the index finger is pressed firmly on the rim, as is the pad of the middle finger. The bend in the index finger can then be used to support the disc, while the wrist can still be cocked well back for a power throw. The disc can be held out flat and ready to throw, which makes it a good grip for throwing the high forehand.

Other Grips

The grip shown at right is an interesting way of helping improve forehand throws in weaker players. Instead of the pads of the fingers being against the rim, the side of the middle finger is against the rim. This grip promotes a palm-up follow through, and helps stop people from turning their forehands over on release. The down side of this grip is that the snap puts lateral pressure on the finger joints, and persistent hard throws using this grip can damage the joints. It is therefore only recommended as a teaching aid, and not for use by experienced players.

Endless variety is possible, particularly with fine-tuning. Most people use one of the above basic grips, but with their own minor adjustments. With regard to radical differences, few are of practical use. The only alternate grip to those above which is sometimes seen is the use of one, three or even four fingers inside the rim instead of two. Fewer fingers for some reason seems to give better control and accuracy, but using only the index finger puts a lot of pressure on just the one finger, and this is probably why it is not commonly used.

Hammer Grips

These are essentially the same as for the forehand. The significant difference is that the hammer throw is released upside-down, so that support underneath the disc is not as important as for the forehand. A tight grip with the thumb is important, since it is the digit which is doing the supporting. This makes the power and hybrid grips the better choices for the hammer. The harder the disc is thrown, or the more wind you throw into, the more vertical the disc should be when released.