I looked a little harder.
I don't have any jig borer reamers, but Robert's photo does not show a reduced shank behind the flutes, although it could be the angle. I do have straight chucking reamers, none of which have cutting edges on the face or a larger center hole (only a small center hole used to support the reamer during grinding).
On the other hand, all of my counterbores have cutting edges on the end and large, deep center holes (1" CB):
@rwm, could you provide a side view of the cutter?
I also dug a little deeper: I did find some photo's of "Jig Borer Reamers" showing the ends (quotes because I couldn't find any from a manufacturer), and they do show cutting edges on the end, but not extending deep to the center, more like what you see on a HSS shell mill. There is also a larger center hole, but not as deep as what Robert's photo shows.
Looking for what these reamers are, I only found one
explanation for the difference in construction: short stiff shaft and end-cutting to precisely locate & ream the hole because the "drilled hole may be off location a little:" this doesn't make sense to me, because if you are using a jig-borer, all of the operations should be equally precise, and you wouldn't want the final, operation to be the one that determines the location & size. The only "authority" that I found was Moltrecht (
Machine Shop Practice, 2nd Ed, V1, pls 436 – 437), and he doesn't say anything about end cutting.