Gone means they left in the past and are there now. "Paul's gone to the shop"
Been means they left in the past and came back in the past "Paul's been to the shop".
Both are Present Perfect because an action which happened in the past has an effect now.
You can't speak to Paul now because he's gone to the shop.
The fridge is full now because Paul's been to the shop.
That's why we say "have you ever been to Paris?" (because you're here now) and not "have you ever gone to Paris?".
For a lesson I would teach gone and been separately, providing students speaking practice for first gone (e.g. students mingle with different situation cards - "I hear Paul is ill" answer "yes he's gone to the hospital" etc etc)
and then with been something similar, ("you look brown!" answer "yes I've just been on holiday" etc etc)