Mashing is a specific form of steeping, but steeping does not necessarily imply mashing.
Certain types of malts have undergone a sort of "pre-mashing" during their production, so their starches have already been converted to sugars by the maltster. You only need soak the grains in some hot water to release the sugars. Think all of the caramel (crystal) malts, chocolate malt, and so on.
Mashing is where you steep grains at a certain temperature (or series of temperatures) for a specified amount of time. This allows enzymes present in the malts to break down starches into the sugars that the yeast will ultimately ferment into alcohol and CO2. You have to do this with all of the "base" malts like pilsner, munich, and pale malt.
When you steep, you're generally looking to get color, flavor, and some unfermentable sugars from the grain. When you mash, you're aiming to get yeast food.