I have a problem with what I suspect to be an incorrectly installed
shower drain. I've visited the local home improvement stores to check
out the parts of a shower drain, but still couldn't figure out how the
drain in question was put together.

Here's what the problematic installation looks like:

The strainer is a typical metal strainer with small metal "tabs" bent
towards the drain. (I don't know what the "tabs" are properly called,
but apparently they are for securing the strainer to the drain by friction).

The shower drain (housing?) is a typical design made with PVC. The wall
of the cylindrical hole in the middle of the drain forms the "outer
ring" of a 3-ring concentric structure (as viewed from the top).

The "inner ring" of the 3-ring structure is a PVC drain pipe.

Between the inner and outer rings is a black ring? or cylindrical? part.

The problem: the tops of the middle and inner "rings" is too high,
interfering with the "tabs" of the strainer.

(I'm going to post a crude ASCII-art drawing of the drain in a follow-up
message.)

Can anyone make sense of my description? If so, what is wrong with the
installation? What is the proper way to fix it so that the strainer can
be securely put in place as it was designed to.

Thanks.