Honestly, there is very little difference between Kickboxing and Muay thai, aside from the Elbow rule.
A couple decades back, kickboxing used to be it's own sport, with Karate/TKD guys & boxing thrown in. Nowadays there is a VERY heavy Muay Thai influence in kickboxing. Kickboxing also contributed to the punching techniques in modern Muay Thai.
It really is one big clusterfuck. Almost everyone that considers themselves a kickboxer uses Thai kicks nowadays, with a little Karate or whatver thrown in.
Most Pro kickboxing matches utilize leg kicks. Guess where they got them from? I would consider K-1 Kickboxing.
Dutch Kickboxers also consider themselves Muay Thai practicioners too. But they're style is different, it has strong Japanese influence with roots in Kyokushin Karate, Muay Thai, and Boxing. That's why if you go to a dutch gym, you will notice that some of them count in japanese. Or do traditional Japanese MA customs like kneeling and bowing.
For me, i just consider Muay Thai as a style with Lots of Clinching and Elbow practice. Everything else is Kickboxing. It's easier that way.
The lines are really blurred on this subject.