Mouse speed is how far the cursor moves for some distance of physical mouse movement. Mouse acceleration additionally makes the cursor's speed increase when the mouse's acceleration (change of speed over time) is faster.

Mouse acceleration is annoying (bordering on infuriating, imo) because it changes cursor movement from an easy 1:1 mapping of mouse movement->cursor movement by adding an additional dimension. You then not only have to keep in mind how far you're moving your mouse, but also how quickly you're moving it. I can't fathom why UI designers seem to think that it's so great that it should be present with no ability to disable it.