I think the names "theme park and "amusement park" are kind of even self-explanatory!
Theme park is about theme and immersion (which can be done through thrills, shows, grand sights, slow rides or other attractions), like Disneyland (and all its sister parks), Epcot, Disney Hollywood Studios, and all the Universal Parks, as well as a few of the "none famous" parks in Europe and Korea.
Amusement parks are parks with mostly generic thrill rides or carnival/off the shelf rides and occasionally have a licensed brand name/character slapped on the entrance to make it more themed. Basically, Six Flags and any other similar park.
I still count a park like IOA or DCA a theme park even if it has a few amusement park thrill rides since they're still more themed than not. (Although DCA was borderline amusement park in 2001...)
Parks like Knotts, SeaWorld, and Disney's Animal Kingdom are hybrids. Knotts is trying to return to its theme park roots, and SeaWorld/DAK are zoo/theme park hybrids (even if DAK always claimed "NaüghtAhZoo" or whatever when it opened lol)