The two main categories that bits fall into, are the snaffle bit and the leverage bit.
First lets start with how to define a snaffle.
A snaffle is designed so that the reins have direct contact with the horses mouth. A snaffle does not have a shank and applies no leverage. Most snaffle mouthpieces are jointed in the middle and work much like a nutcracker would. Some snaffles are made with a solid mouthpiece but these bits are primarily used for driving horses in harness. The primary pressure point of the snaffle is the tongue followed by the bars of the jaw and then the corner of the mouth.