Fast-medium is a pace bowler who bowls slightly slower than a true 'express' fast bowler and relies more on seam and swing to get his wickets. Virtually all international pace bowlers (ie not spinners) are 'fast-medium' with only the odd true 'fast' bowler playing today.
Medium-fast is generally a part time bowler who is normally in the team mainly as a batsmen, but bowls quicker than the usual 'military medium' most part timers bowl. Specialist bowlers are never 'medium-fast' and it would be an insult to call one such.
Of other terms used, 'medium' is the pace a typical part time bowler bowls, while 'slow' is just another word for a Spinner. The terms 'slow-medium' and 'medium-slow' are archaic - if you spin the ball you are a slow bowler, if you dont you are at least a medium pacer, whatever speed you bowl at.