There's
1.) parallel
2.) nock taper
3.) barrel taper
4.) full length taper aka rat-tail taper?
5.) breasted taper ?

What shape is a breasted taper?
Any others I may have missed?

Thanks

1.) parallel > did not know that was a taper


6) point taper

Breasted and barrel taper are the same,usally the last 9-10 inches is tapered down to 5/16 for the nock end and the front about 8" is tapered down to 11/32" for the point end on a 23/64 shaft.Some called it barrel and others call it breasted.Nock taper is just the taper for the nock.Parallel is just a straight shaft.Full taper is tapered from the point end down to the nock.

On a breasted shaft, the large-diameter section is further toward the fletching than barreled. Barreled has tapers that generally are about the same length, but the point taper may end in a larger diameter. Breasted has a shorter taper on the fletching end, longer on the point end. Originally designed for flight shooting with very small points. No FOC.

7. Single taper. Only the fletching end is tapered.

Lets step back a little into history. Here I have the nomenclature as given by FORD (1880):
 

Ol' Horace could shoot 'em.