Mineral spirits and paint
thinner are the same thing. Used to thin paint (duh); cheaper than turpentine, which used to be the thinner of choice for oil-based paint.
Lacquer thinner used to be 100% MEK (Methyl Ethyl Ketone), but I just looked at the ingredients in the can I have in the shed, and it's got all kids of stuff in it.
Acetone is the stuff that your chemistry teacher poured on a Styrofoam cup to make it dissolve and impress the students on the first day of class. I think it also used to be used as shellac thinner, but I've never used shellac.
Paint remover is a very broad term describing a variety of products used to...I forget what.
Fortunately for us, gelcoat is impervious to a lot of chemicals, so we have a lot of latitude to experiment.