I don't think there is a universal definition for kickboxing. In japan there is japanese kickboxing that uses elbows, which is different from K-1 style kickboxing without elbows. Then there is also WAKA kickboxing with no kicks below the waist, no knees, no elbows.
Most kickboxing today is inspired by K-1 style kickboxing but with some differences.
In the end, most different styles have some lap overs and similarities it's not black and white. There are some good threads in this forum about the history of dutch, japanese and american kickboxing. Does anyone have a link?