Muay Thai is the traditional Thai art that uses kicks as well as punches and elbows and knees during clinches. Kickboxing is a catch all term for fighting in the ring with kicks and punches.

kickboxing = bad leg kicks,no elbow,no knee and some good punches

muay thai = deadly leg kick,elbow, knee and some good punches

muay thai is better than kickboxing

but western boxing has best punches

so muay thai and boxing are good

kickboxing suck better than karate and kung fu thow

Same sets of techniques different rules.