As far as I'm aware, the "military" bit is one of the few whose name refers to the way the tenon-end of the pipe meets the pipe shank. There are also "thread" or "screw" bits, which actually screw into the shank (fairly common on meerschaums but not on anything else). All of the other bit names refer to the overall shape of the bit or the specific shape of the mouthpiece. Nowadays, you're not likely to see an orific bit, which is a round hole at the end of the mouthpiece (rather than a broad opening). Most common is the wedge bit, which if extended a little on the sides might be called a "fishtail." You're also likely to encounter a steck bit, which features a hole on the *top* of the bit, for projecting the smoke to the roof of the mouth rather than the tongue. (Handy if your tongue is tired out.) These are most popular on Peterson pipes and, due to their shape (and the strong Peterson association), are also called P-lip bits.
Bob