Muay Thai teaches simple and straightforward fighting techniques that are effective and easy to use in a real fight. Thai kickboxing doesn't focus on some fancy looking moves that are not very effective.
Muay Thai puts a great pressure on conditioning: stamina and strength training, shin conditioning, core conditioning. This gives you a physical advantage over the potential aggressor.
In Muay Thai the main tool of learning is sparring, which means you’ll be encouraged to fight almost right from the beginning of your training. You’ll have to face a real opponent instead of punching the air. This gives you a great mental advantage over the attacker
I have created a post: Muay Thai for self-defense to cover this subject.
In street fight, you have to be able to move around freely and be able to defend against more than just one opponent. You need to be able to look around, evade, and react quickly.
You don't want to find yourself in a situation where you are sitting on a guy and punching him or holding him down on the ground and some other guy walks in and "soccer kick" you in the face.
What works in the octagon doesn't necessarily work on the street. That is why a stand-up fighting style like Muay Thai is much more effective for the street than a grappling style like BJJ [Brazilian Jiu-Jitsu].
Muay Thai utilizes 5 main sets of techniques from which everything else derives:
There are quite a few of them and most of them are very spectacular:
Also: Who was the founder of Muay Thai?
The predecessor of Muay Thai style called Muay Boran can be traced to XVI century Siam - now known as Thailand - where it was developed as a deadly martial art that can be used on a battlefield.
Muay Boran wasn't limited by any rules and the sole purpose of that fighting style was to kill or maim the enemy soldiers using any technique available, including head-butting and other brutal strikes. It was an aggressive and a very effective style and a lot of Muay Boran fighting techniques can still be observed in modern Muay Thai.
I wrote more about this subject in History of Muay Thai