"Take a plane" would be used more when you are just describing your mode of transportation. "How are you getting to Cleveland?" "I'm taking a plane on Thursday." "Catching a plane" is used more when the mode of transport is known and time is a more of a factor. "Can you stay a while?" "I'd like to, but I can't. I have to catch a plane at 4:30." or "Can you be home tonight?" "It depends on whether I can catch the 7:30 flight."