The drop-in sink is also called semi-recessed because 2-3" of the sink is above the counter and 2-3" below the counter. The Kohler Serif and Yin Yang are examples of this style. Some have faucet decks and some don't.

Self-rimming just have the rim sitting on the counter, supporting the basin which is entirely below the counter.

I'm looking at drop-in sinks for a couple of built-in vanities that are too short for us but we're not going to replace them, so the drop-in sink with a faucet deck gives us several more inches in height.

Of course, both styles mean you have to clean around the sink rim, not just sweeping into the sink like you can with an undermount sink. I'm willing to do the extra work to save our backs but YMMV :) .

HTH

Self-rimming and drop-in are indeed the same in terms of how they get installed. A hole gets cut in the countertop and the sink dropped in the hole from above, the raised profile edge on the sink rim creates its own rim.

To pick nits, stainless sinks have a low-profile "rim", cast-iron and ceramics have a higher profile rim. Some designers used to refer to all of these "installed from above" sinks as "drop-in", but only the ones with higher rim profiles were "self-rimming".

Today, at least in my realm of work, all drop-in sinks are referred to as "self-rimming".

Their counterpart is the undermount sink. Installed from below.

Or apron-front sinks, which are farmhouse style sinks.

Vessel sinks, some trades-folk refer to vessels as surface-mounted sinks.

But overall you are correct. "Self-rimming" and "drop-in" are essentially the same thing.