Are there any differences between turbofan and turbojet engines besides bypass air? I think I understand both engine types, but I am just wondering am I right in saying that the only difference between the two types of engines is the bypass air (i.e. a turbofan is just a turbojet engine with bypassed air).

If not, what are the other differences between the engines apart from the bypassed air?

Any help on this matter would be much appreciated.
You are right about the bypass being the same result as a tubofan.
However the word turbofan refers to an extra turning bladed wheel in front of the compressor and larger in diameter it turns slower and moves air past the engine on the outside.