Long articles and books could be written on the differences between these different disciplines. Here, we just want to summarise the key features.
Powerlifting is a strength sport that consists of three attempts at maximal weight on three lifts: squat, bench press, and deadlift.
Olympic weightlifting, is an athletic discipline in the modern Olympic programme in which the athlete attempts a maximum-weight single lift of a barbell loaded with weight plates. The two competition lifts in order are the snatch and the clean and jerk.
CrossFit is a branded strength and conditioning program consisting mainly of a mix of aerobic exercise, calisthenics (body weight exercises), and Olympic weightlifting.
CrossFit usually involves some Powerlifting and Olympic weightlifting moves along with additional barbell moves such as Thrusters. Cross Training or Functional Training often refers to exercises similar to those used in CrossFit, but not carried out by an official, banded affiliate of the CrossFit corporation.
Bodybuilding competitions are decided by the impressiveness of the contestants visual appearance and stage poses. Bodybuilders often use free weight exercises to attain the physique they want and usually also incorporate weight machine exercises to isolate a particular muscle they specifically want to sculpt.