The two can be used synonymously, but there is generally a difference at least of degree between them, and often of intended meaning.
To "misuse" is "to use incorrectly". For example, if you take a screwdriver and try to use it to paint a picture, you are misusing it; the screwdriver is not designed for painting, and will not do a good job when pressed into that service, but neither the paint, the picture, nor the screwdriver will be damaged as a result of your action.
To "abuse" is "to use excessively or damagingly". For example, if you take a screwdriver and try to use it to pry up a manhole cover, you are abusing it; although a screwdriver can often be used to pry up small objects, a manhole cover is much too large for an average screwdriver and you are likely to end up with a bent, damaged screwdriver and an unmoved manhole by the time you give up.
In terms of sociology, as @Daniel has also said, the usage is essentially the same, although I'd say you are much less likely to encounter the word "misuse" in this context (or if you do, it is entirely synonymous with "abuse"). If an employer makes his workers engage in a dangerous action without taking appropriate safety precautions, he is abusing the workers ("using them in a way likely to cause damage"), even if they don't actually get injured.