I'm surprised I couldn't find a clear and precise answer for this on the net. Some guys claim that the difference is only a matter of AmE/BrE English, while some other guy has suggested this example on a forum as to explain the difference:
a) You would have to turn round the bend and drive straight for 200 meters before you arrive at the gas station.
b) Please turn around and let me see your back. (A circular movement around a fixed point)
I wonder who is being correct? Just recently, I myself had learned about "turn round" in my English book too, and it denoted the same thing as the case "a" above (changing the direction, while driving, in order to get back to somewhere.)
Best Answer
There is no difference. "Turn round" is the same as "turn around".
Some American dialects will write the expression with an apostrophe ('round) to indicate it's an abbreviation of around and distinguish it from round (meaning "circular"). In British English it's simply written "turn round".