Both of them fall under the erosion style called mass-wasting, then under the subdivision of landslide slope failures (the other being sediment flows). Slides differ from slumps in that there is no rotation of the sliding rock mass along a curved surface. There are two graphics below that will show you, if my explanation doesn't make enough sense either.
(1) Slumps (also called rotational slides, obvious if you see it from the side) are a type failure where downward rotation of rock or soil occurs along a concave-upward curved surface (rotational slides). So think of a very flattened skateboard half-pipe, and then another and another nested in each other. The blocks themselves (each half-pipe) stay pretty much the way they were, but they just collapse downhill, like when a deck of cards gets away from you, but with the curved shape added. Slumps leave these curved scars on the hill's slope. They can be isolated, or can also occur in large complexes covering thousands of square meters. They often form as a result of idiot human activities, and so are very common along roads where slopes have been cut wrongly during construction. They're also common along river banks and sea coasts, where erosion under-cuts the slopes. Heavy rains and earthquakes are often the trigger for slumps.
(2) Slides (also called translational slides) are rock slides and debris slides that happen along a pre-existing failure surface (a weak area). These can be bedding planes, metamorphic foliation, sediment beds, and joint surfaces. Sometimes soil sitting on an otherwise bare rock face. You'll usually see piles of debris (talus) at the base of the slide, or an area that is prone to sliding.