One uses the parenthesis and not the other, but what are the differences of using either?
won't do anything. The parenthesis cause a function to be called.
Having a statement consisting of nothing but an identifier (be it a function name, variable, or whatever) won't do anything (except throw a reference error if the variable doesn't exist).
And what happens if i dont use any href attribute?
Then I'd question why you were using an element in the first place.
And also, is there a difference on assigning a inline onclick function to an anchor (a) that to other elements (e.g. span div label etc)?
Only that they aren't (by default) focusable elements (nor is an a element without an href attribute), so the click event couldn't be triggered by tabbing to the element and pressing enter. If you want an element that will do something with JS when triggered, and you don't have a sensible fallback for when JS isn't available, use a button.