Catch up means to get back at pace. The best way to describe it is like this; imagine you and a friend are walking on the side walk, you're friend begins to walk a bit faster. In return you speed up to make sure you are with your friend. The act of getting back to where your friend was is catching up. Keeping up would be to stay with your friend the whole time.

Catch up is also means to be up to date (I have to catch up with my work first) Keep up: - maintain/continue (..keep up the pressure until..) (keep up doing the good work!) - go with the same speed (..keep up with the train..) - hold upright (keep your hands up)

a. To get and hold (something that has been in motion) in a hand, the hands, a container, or an implement: caught the ball in the web of the lacrosse stick. b. To take hold of, especially forcibly or suddenly; grasp: caught me by the arm; caught the reins. c. To stop (oneself) from doing an action: I caught myself before replying.