The tapper came with, IIRC, 6 different capacity collets to drive up to 5/16" taps. The 5/16" collet is very thin in important places and is commonly missing on the used market or broken. Again, IIRC, the tool has a pin across the bottom of the collet chuck and the collets have a slot in the bottom. The knurled nut has an internal taper to squeeze the collet and retain the tap. I'm sorry for continuing to use, IIRC, the chuck shaft on the screwdriver does pull out further than the tapper, but I'm really uncertain about that.
I've never used the screwdriver type tool, so I don't really know how it's supposed to operate. It doesn't make sense to me that the front shaft has to be pulled out to reverse rotation, because when driving a screw, you have to apply pressure whether driving it in or out.
Pulling out the shaft is what was meant when I wrote "quill up" regarding the tapper operation description in reply #7593.
I have more than one of each type tool but they are in WA, and I'm in CA right now, so no pictures from me today.
I think I bought the first screwdriver by mistake (thinking it was a tapper) and decided it would not be a great tapper for reasons that I can't precisely remember right now, except to say that there are more differences between the two tools than tap holder collet chuck vs screwdriver bit holder.