Welcome to GIMPtalk!
Well, some types off the top of my head:
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Procedural brushes -- these are simple geometric shapes (circles, squares etc) with varying level of hardness and size. They are created in GIMP's internal brush editor. Their main advantage is that they can be dynamically resized to any size without loosing quality (since they are just described by a mathematical formula, essentially). They are commonly used for all forms of painting and line work that involves applying a chosen colour onto the canvas in any form and mimics simple painting tools like round brushes, felt pens and the like. They are saved as gimp brushes (file ending .gbr)
Image brushes (black & white) -- these are small black images of any shape on a white background. Their black areas will be replaced by the chosen colour and the white will be transparent when used. These are used for all sorts of things; with wide spacing they can be used to apply textures and shapes (it's more like a "stamp" than a brush in that case, or they can be used to mimic natural media effects, like charchoal pens or strands of grass. File ending .gbr.
Image brushes (coloured) -- these are often cut-out pieces of an image used as a brush. Since they are already in colour, they are unaffected by what colour is currently is chosen, but will simply repeat the same image over and over with the chosen spacing. In GIMP2.4+, the last selection copied to the clipboard will automatically appear in the top left of the brush list to be used as an image brush. It's primary use is to make repeating patterns, for example a tree full of identical leaves, or stamped down one at a time for special effects like stars or flowers or similar. File ending .gbr.
Animated brushes (Image hoses) -- Animated brushes consist of a series of images in a series. They can be black&white, which means they will be affected by the chosen colour, or coloured. An animated brush will loop through its animation cycle in different ways depending on its settings (defined when saving the brush), and can have many different animation paths to take (for info on setting this up, see the GIMP manual). The correct name is really "image hose", and they are saved in files ending with .gih .
The simplest Image hose just loops through its animation every time its applied to the canvas (set by the brush distance). This can be used to have brushes that change repeatedly -- making the leaves of a tree more varied by pasting different tree images for example.
More complex image hoses might be sensitive to the direction you move the mouse, showing different animations depending on that. An example would be the classical footprint brush that has foot prints appearing one after the other (that is, combined with a cyclic animation of the left and right footprint appearing) and always turning in the direction of the mouse movement. Even the velocity at which you move your hand can be made to affect the brush's look.
Animated brushes are also GIMP's way of implementing custom tablet sensitivity in brushes. GIMP senses all the special features of tablet pens, such as tilt, rotation, and pressure. These can be used for implementing natural media brushes, like a brush that changes shape when pressed down harder, or becoming wider when you angle the pen to the tablet, just like a real tool. Unfortunately the implementation is complex and the library of good animated natural media brushes for GIMP is not very large.
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Hope that helps.
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Griatch
