According to my textbook:
A function which has either $\mathbb R$ or one of its subsets as its range is called a real valued function. Further, if its domain is also either $\mathbb R$ or a subset of $\mathbb R$, it is called a real function.
As there are 2 definitions here, is there a difference between "real functions" and "real-valued functions"?
MathWorld says that a real function is also called a real-valued function.