The Bit Gallery
The names of the various types of bit are taken from the characteristics of the bit in question.
To give a more accurate description, the full name of the bit may be taken from both the rings and the mouthpiece. This makes for some long names sometimes, but by breaking the name down, you can tell what characteristics it has. Conversely, you can look at a bit's characteristics and come up with a name for it!
For example, we'll take the Full Cheek snaffle, named for the cheek extensions on either side. Combine that with the eggbutt connection and you've got a full-cheeked eggbutt snaffle.