Its like one of those logic questions...
in my opinion, all Theme Parks are technically Amusement parks, but not all amusement parks are Theme Parks.
Going back to the earliest part of the 20th century, the great Coney Island NY parks all tried their hand at Themeing. By today's standards, they were week, but they did what they could at the time. Even today in your "traditional parks" you do see some theming. Kennywood does it mainly in their "Lost Kennywood" section. (I don't count Exterminator... it is a themed ride, but the theming ends with the ride). Hershey does it with some of their areas (Tudor Square, Rhineland, Minetown, Pioneer Frontier, Tower Plaza, and Midway America. Comet Hollow and Music Box Way seem to be just names of areas, no theme), but their theming is MINIMAL at best. They, like Kennywood, have done their most extensive themeing in their area that is to look like an amusment park of the past (Midway America). Is this Theming? Technically, yes. But compared to places like IOA and Disney, it is nothing!
To me, it comes down to this. If the main attractions are the rides, then it is an amusement park... if the attractions are the rides and the surroundings, then it is a Theme park.
(not sure any of that made sense... I really knew what I wanted to say, but it doesn't seem to have come out right)
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"Resistance is futile... you will be assimilated." The BORG's (and Six Flags') motto.