What is the difference between operator and function?
Historically, my guess is that the difference is rooted in how things were (and still are) translated into machine code.

An operator such as addition of integers or exclusive-or of booleans would be translated into one (or few) assembler commands which would be directly executed by the processor (resp. its ALU). It would also be part of the syntax.

A function (or procedure, method), on the other hand, is a subprogram the (main) program would explicitly jump to during execution. That is, a new stack frame is allocated, register values are saved, parameters are passed and only then is the function executed. See here for details. Furthermore, functions are defined by the programmer.

Younger programming languages have introduced more abstraction, partially or totally removing the distinction. In C#, for instance, you can overload operators for your own types. In Scala, there are no operators but only syntactic sugar for binary methods. Once these languages are compiled, though, you can see which language elements are translated to flat instructions and which to subroutine calls. Keep in mind that optimising and/or just-in-time compilers may liberally move between worlds.