When you do Taekwondo, you are allowed to do different kicks and punches to the upper part of the body. When you do Muay Thai, this means that you can make different attacks on the various body parts of the person that you are competing with. These martial arts are usually learned by people in order to improve themselves. Some would enter competitions because of it.
There are also others who would learn how to do martial arts so that they can defend themselves whenever they need to do so. Muay Thai is a bit trickier to learn because you need to mix attacks to reach various parts of the body. The opponent will find it harder to defend himself since he does not know where you are going to attack next.