This is at the bottom of a kitchen sink water pipe, where it connects to
a pipe that comes up from the floor. There is an adaptor that seems to
go over the pipe from the floor and have threads above for a nut which
might be for compression.

The pipe to the sink seems to be flared inside the threaded part of that
adaptor. The compression nut can be loosened and moved away from the
adaptor, riding up the pipe towards the sink, till you let go of it and
it falls back down. (I'm just trying to make the picture as clear as
possible, so ignore the parts that are too obvious) With that nut up out
of the way, the flared pipe won't pull out easily, probably because the
pipe is stiff, and/or the flare inside the threaded part is too tight
against it.

Keep in mind that the threads are on the outside of the adaptor, and the
flare of the pipe from above is on the inside.

There is no obvious way for the adaptor to connect to the pipe below. It
looks like it just sits on it like a sleeve, but it won't pull off, nor
turn in either direction. There is no obvious solder. As far as I can
tell all pipes are copper, but the one to the sink above seems to be
tinned or something, and only the flare looks like copper.

I'm afraid of turning anything too hard, because the pipes are small and
old, and might break. The floor is a slab foundation, and the pipe
coming up through it can't be easily replaced.

I basically want to replace as much of this stuff as possible, because
it's old and hard to work with. I want to replace the pipe to the faucet
with a flexible pipe with female npt connectors at each end, which comes
in a package labeled for the purpose of connecting a kitchen sink faucet.
But before I can replace anything, I have to remove the old stuff without
damaging anything that can't easily be replaced. And before I can remove
it, I have to understand what it is, so I can remove it without any such
damage.