The "functional sense" is the one that's underspecified for system programming. For example it considers allocation a pure operation, but that's actually implemented by modifying a global variable so how is it pure? One might argue that it's not observable, but so is printing to the console, which is usually taken as an example of an impure operation.
It's true that these are all somewhat related concepts, but I'm pretty sure the term "side effect" is consistently used in the functional sense.