Just=only but not always!
just=very recently: I've just done it
just=only: we will just have 2 cups of tea, please.
just=fair: I am not a just teacher!
just=simply: just tell me what you need.
just=at the exact time: just when you come home, give me a call.
just=right at the point: he was just about to go out when....
You are my only hope, not my just hope, here "only" modifies a noun.
When "only" is an adverb, just=only but not always.
She only comes to see me when she is in trouble. (the activity is limited to..)
She just comes to see me when she is in trouble. (at the exact time)
I think it is fair enough to get you started. Perhaps other teachers will expand on it.