This is the diference:

american kickboxing (kickboxing) - is a free style sport,kicks and punchs over the waist, no elbows, no knee,no groin strikes.

Muay Thai (thai kickboxing)- allows punchs, kicks (low,high,anywhere),elbows,knees,no groin strikes.

There is also french kickboxing (savate),japanese kickboxing (shoot-boxing),chinese kickboxing (Sanshou), and the list of styles and rules continues…

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