Hi there,
Don't make it too complicated for yourself, they both mean the same! The word "before" in this context simply means "at some point in the past". **Before can also be used other ways** However (in my opinion) "I did it before" does not sound very educated and might not be grammatically correct. I'm sure people do say it this way. "I've done it before" is a better way of stating it.
Here are some examples :
Have you been to London before?
Yes, I have!
Have you ever done something like this before?
No, never!
I've done this kind of work before, but it was never this hard!
Oh, really?
Let me know if this helps!!