Think of it this way…
If the lid takes 3 turns to remove, then only the first 'grab' will loosen it, but after that it still needs unscrewing the other 2.9 turns To actually ask someone, either version would probably do - they'd be aware that you were asking because you were having difficulty with that first part, not that you couldn't be bothered with the other 2.9 turns ;-) "
Could you open this for me?
" would also work just fine, by the same assumption.
ell.stackexchange.com/users/11747/gone fishin' again.
Assuming you mean in normal conversation.
They mean pretty much the same thing.
If a asked to loosen a cap for someone I would turn the cap till is was almost off, then hand back the bottle.
If asked to unscrew a cap, I would fully remove the cap, handing them back the bottle and the cap in two separate pieces.
That said, they are really quite interchangeable, and a person may do either one if asked either way.
It just depends on the person.
If you mean in some kind of technical document, or instructions it would be normal to see something like
"Loosen the cap until product is accessible, but do not remove the cap completely.
"
"Unscrew the cap completely to access the product.
Once finished replace the cap.
"
Point being that even in technical documents the loosen/unscrew verbs are usually modified with further instructions to clarify the partially on or all the way off part of the definition.
ell.stackexchange.com/users/20589/coteyr
"Loosen" means that the seal of the jar will be broken, but the lid will be left on the jar.
"Unscrew" implies that the lid will be removed.
ell.stackexchange.com/users/18653/dennisdeems
"Unscrew" is valid if the cap is, in fact, a screw type.
(Though you probably only need assistance in loosening it, not completing the job.)
If it's some other kind of seal, "loosen", "open" or "undo" might be more appropriate.
ell.stackexchange.com/users/20585/Rocker
Unscrew indicates the lid/cap and container are of the screw variety.
Loosen doesn't imply that the lid/cap must be of the screw type, it could be held on by friction.
Loosen also sounds less than completely remove.
One might loosen a screw in order to make room for something else to fit on it without removing it completely.
Unscrew without any other modifiers has more completeness implied.
ell.stackexchange.com/users/20591/roymeo
For example, could you help me "loosen" or "unscrew" this lid/cap? Which one is correct and more common?
What is difference between "loosen" and "unscrew" for lid/cap?
ell.stackexchange.com
<phrase-usage>
ell.stackexchange.com/questions/59654
ell.stackexchange.com/users/20274/Little_Grass
Although they are very similar, "Loosen" implies that the seal of the jar will be broken, but the lid will be left on the jar.   "Unscrew" implies that the lid will be removed completely to access the product. Loosen means that the seal will be broken but the lid will not be removed. Unscrew implies complete removal of a screw lid.
Loosen means that the seal will be broken but the lid will not be removed. Unscrew implies complete removal of a screw lid.