I' not an expert, but I'll weigh in;
chop saw- body of the saw moves up and down in a arc- cuts 90 degrees
miter saw- body swings in an arc horizontally lockable to various
degrees, as well as what the chop saw does.
compound miter saw- does everything the last 2 did + the body also
rotates side to side.
sliding compound miter saw- does every thing the last 3 did plus slide
in and out against the fence, perhaps combining the chop at the
beginning of the slide to cut a really big board.
The best thing about the sliding compound miter saw is that before this
was offered you need a really big blade to cut larger pieces, 18"
blades weren't uncommon where big stuff was being cut.