OK. I won't be such a jerk. I seriously wouldn't advise you to include them into your routine, but, if you want definitions, here they are:
Standing Leg Curl: Usually done with a cable. It involves drawing your heel up to your butt against resistance.
Single Leg Extension: You do a leg extension (on a leg extension machine which you can google) with one leg instead of two.
Standing Calf Raise: Possibly the only slightly useful one of the bunch. You stand on a raised platform (stairs, box, bench, whatever) with your toes and the balls of your feet only. The rest of your foot hangs off. Then you raise your heels. You can google pics of this, too.
Seated Calf Raise: A calf raise done on a machine which allows you to mimic the motion of a standing calf raise from a seated position.