If you go back far enough, Kickboxing was the terminology used for an American style of fighting that was basically punching and kicking, but all above the waist. Every punch and kick had to be from the waist up and included the face. It was a style of fighting with that rule set; it was limited to that. We call Kickboxing 'the style of the four weapons': two arms and two legs, punching and kicking.
Muay Thai comes from Thailand and it is the style of the eight weapons. It includes punches, elbows, kicks, and knees, so you have double the weapons. Also, you're allowed to attack any part of the body. You can kick the legs. You can knee, elbow anywhere, and also you're allowed clinching. That means you can grab somebody, throw knees, throw elbows. Basically, you have a lot more options.
This is how everything works in martial arts, especially from a competitive point of view. As soon as you add in more weapons, the fight usually ends faster.
In boxing, you'll see these guys going 15 rounds because they just have two weapons. With Kickboxing, where you have punches and kicks, you'll see the rounds shorten up. The chance of a faster finish is much more likely because there are more weapons.
Then there's Muay Thai. These guys can punch, kick, knee, elbow, and use those weapons everywhere. You end up seeing even shorter rounds because the odds they can finish fast are higher.
When it comes to martial arts, the more weapons you have, the more chances things are going to get finished soon.
“They have Muay Thai, Brazilian Jiu-Jitsu, and wrestling. They welcome children and beginners with open arms and all the staff are extremely knowledgeable.” -Shane G Risler