Yeah there is. 'Pick it up' can have more than one meaning. For example, pick up that pen, please. Literally means, pick it up with your hand, but in this context (with the computer manual), it means that you will understand it. So it's more of an abstract meaning I guess.
Hang it up is completely different. Hang up your coat (put it in the wardrobe, or on the coat rack), or sometimes it might be used to say that someone is quitting or retiring ...For example, Messi has decided to hang up his boots (retire from football).