What is a loop variable?
The term that I was taught (thanks, Dragon Book!) is "induction variable". It refers to any variable which is a linear function of the number of iterations in a loop.

I don't know the term "loop variable", but if I had to guess, it would refer to a variable whose value changes inside the loop, and which is tested to decide the loop termination condition.

But to be honest, it would depend what you were trying to use it for. Pick whatever definition helps your analysis.