badminton与shuttlecoke, Pingpong与table tennis有区别吗

badminton is 羽毛球
http://www.worldbadminton.com/

shuttlecock is 毽 or 板羽球 (http://www.rsljapan.com/photo/shuttlecock.jpg)

ping-pong/table tennis is 乒乓球
http://tabletennis.about.com/

跳绳 = jump rope or skipping. If you mean the game a lot of Chinese girls seem to play maybe the English name is different, because I only saw this game in China I don't know the English.

Jump rope, also known as skipping rope or skip rope, is a game played primarily by children wherein one or more participants jump over a spinning rope so that it passes under their feet and over their heads. This may consist of one child twirling and jumping the rope, or with a minimum of three children