Okay, here I go yet again -- but I just have to ask: Butt chisel vs. bevel edge chisel -- how are they defined and what's the difference? Mortise chisel vs. sash (?) chisel -- again, how are they defined and what's the difference?

That’s OK… some of it still confuses me these days as there is some overlap between types.  This is just my take on it as terminology by trade and era varies a bit:

Bevel edge doesn't mean much per se, as even some firmer and framing chisels have them... it merely allows getting into a tighter corner. 

Neither does socket or tang handles, although the larger chisels are generally socket chisels, as are many high-grade chisels, as sockets are considered a better design as handles are easier to replace, but cost significantly more to manufacture. 

To call a chisel a “socket” chisel with no other descriptor is a common mistake today, often by people who should know better.

Butt Chisel

Any short chisel, usually with bevel edge and design suitable for paring and striking with 30-degree bevels.  A finish carpenter or shipwright’s pocket chisel easy to store with a major role in hanging doors and all around trimming.  Usually tang handles.

Bench Chisel

Longer chisel for workbench use. Paring and light chopping, usually with 30-degree bevels and beveled edges.

Paring Chisel

Long, thinner chisels not designed for any striking, only paring with 20-25 degree bevels.  Some have "cranked" handles for clearance and were primarily used by pattern makers making negative patterns in soft pine. 

Others are skew cut to reach into corners, and a “dovetail” chisel is diamond-shaped to clean female sliding dovetail sockets.  Usually with tang handles.