When you pick something, you choose it, the way you pick apples in the fall or when you pick a partner to work with in biology class. But if you pick on someone, you bug them in a mean way.
Something you pick can be called a pick, like the "pick of the litter,” the best dog of the bunch. You can also use a pick to chop ice or play guitar. You can pick at something, like a loose thread, or pick something up, like your new puppy. You could pick on someone, but that's a good way to pick a fight, or provoke an argument. Pick is an old word related to “peck, sting, and pinch.”