The main difference between functions and subroutines in Fortran and other ancient programming languages is not the fact that subroutines do not have a return value.

The functions of Fortran are what would be called pure functions in C (which can be marked as such with compilers that support C language extensions, like gcc).

The pure functions cannot modify any of their arguments or any global variable, and they must be idempotent, which is important in program optimization.

This is complete misinformation and you should stop posting it.

One can explicitly declare a function (or subroutine) to be PURE in Fortran, but it is not the default and never has been.