The very important difference is that what are called functions in Fortran are called pure functions in other languages, i.e. functions that do not modify their arguments or global variables and which are idempotent, helping program optimization.

This means that Fortran functions are functions in the mathematical sense. In most early programming languages "functions" were functions in the mathematical sense, while other kinds of subprograms were named procedures or subroutines. The use of the term "function" for any kind of procedure has been popularized mainly by the C language, even if there were earlier languages where all procedures could return a value and even where any program statement was an expression, starting with LISP.

Many C/C++ compilers, e.g. gcc, support language extensions allowing functions to be marked as pure. This is always recommended where applicable, for better program optimization.

This difference is much more important than the fact that subroutines do not return a value.

Many of the "functions" of C/C++ must be written as subroutines in Fortran, with an extra argument for the result, but because they modify some arguments or global variables, not because they were written as "void" functions in C/C++.