Very few exercises are pure forms of those four categories, but there are differences in emphasis which is why we recommend balanced programs of resistance, calisthenics, and cardio training to maintain or improve fitness.
Strength is the ability to move things which resist moving. Power is the ability to move things (including yourself) with speed and force. For example, bench press and rows are mostly strength exercises. Powerlifts are power exercises: deadlifts, squats, military press, etc. in which bursts of speedy intensity are required.
Where would we categorize pull-ups? I'd say Strength.
What’s the difference between strength training and power training?
We have discussed cardio training at length. The main muscle it trains is the heart muscle. While any difficult exercise stresses the heart, only pure cardio training (HIIT via HIIT calisthenics/ aerobics class or sprinting intervals) gives the heart a specifically strength-building stress.
So what about endurance? If you are somebody who "gets too tired" from non-resistance activities, you have an endurance issue. It is not rare for very strong people to have poor endurance or for high-endurance people to be relatively-weak. We want both strength and endurance. Anything that is high-rep builds endurance but not strength or power: long-slow "cardio", high-rep (10-20) resistance work, calisthenics.
One caveat: Do not ever do high-rep (over 10) deadlift sets. The human body is made for low-rep heavy floor lifting (8 or fewer). If you can do over 8 deads, you need to increase the weight and reduce the reps.
