Continuations

http://www.math.bas.bg/~bantchev/place/iswim/conti-disco.pdf

A function returns a value and a procedure just executes commands.

The name function comes from math. It is used to calculate a value based on input.

A procedure is a set of command which can be executed in order.

In most programming languages, even functions can have a set of commands. Hence the difference is only in the returning a value part.

But if you like to keep a function clean, (just look at functional languages), you need to make sure a function does not have a side effect.