wrote ...
I want to add a shower in the bathroom of my office. This is a
commercial structure.

The available copper waste pipe, unlike other pipe compositions,
actually measures 2 inches in diameter. I see in the home improvement
center that the 2 inch ABS is larger than 2 inches.

Technically that 2" copper is tubing not pipe, that being the difference.
Pipe is nominally sized by it's ID whereas tubing is sized by it's OD.

I'm going to use ABS for the shower waste pipes. It looks like most
showers use 1-1/2 inch plumbing.

Why ABS? PVC is a better suited for drain/waste/vent apps.

The sewer pipe coming out of the slab is cast iron, and a copper waste
pipe (from a utility sink nearby) Y's into it using a copper elbow. A 2
inch rubber union (the kind with hose-clamps) connects the copper elbow
to the cast iron Y. I could replace the copper elbow with a Y (copper?)
and run the ABS into that.

How can I mate the ABS to the copper pipe or Y? Are there adapters to
go from one material/size to another (ie, 2 inch copper to 1-1/2 inch
ABS)?

The cheapest and easist way is to use a rybber union as you just described.