Mulch is usually one substance... we lay down leaves or wood chips or straw or something over the soil. It does eventually break down into humus.
But compost is made up of many ingredients, kitchen scraps, fall leaves, weeds, yard wastes, maybe some manure. So the compost contains a much greater range of nutrients from all the different ingredients in it.
For example if you use leaves or wood chips for mulch, they are high in carbon but low in nitrogen, can actually draw some nitrogen from your soil in the process of breaking down (but more so if you till them in, than if they are just sitting on the soil). The kitchen scraps, manures and other things you add to compost are high in nitrogen so the finished product is much more balanced.
So for the original poster: "compost" is the finished product that comes from your compost pile, from the aerobic breakdown of a whole bunch of different ingredients, specifically including greens (nitrogenous) and browns (carbonaceous) (see the greens/ browns sticky at the top of this forum). It can be used on top of the soil as top dressing or in the soil as in putting compost in your planting holes.
Mulch is a layer of organic materials, usually all one kind, that we lay down on top of the soil to suppress weeds, hold water in, etc. They are both important in the garden, but they are different.