Won't

In any cases, the first is an indication of desire and the second is an indication of decision.

I've tried everything, just won't open. (He was talking about a door)

How can a door make a decision?

And can I use both versions interchangeably sometimes?

AnonymousI've tried everything, just won't open. (He was talking about a door)

'Open' is an ergative verb: it can serve both transitively and intransitively:

He open the door quietly.
The door opened quietly.
The wind blew the treetops.
The treetops blew in the wind.
The watch sells for $100.

Anonymous:
I've tried everything, just won't open. (He was talking about a door)

How can a door make a decision?

AnonymousShe doesn't want to pay for it.She won't pay for it.What's the difference between 'doesn't want' and 'won't in such cases? Thanks.

"The door just won't open" has nothing to do with mak

AnonymousShe doesn't want to pay for it.She won't pay for it.

doesn't want ~ She desires not to pay for it. (But she may pay for it even though her wishes are to the contrary.)
won't ~ She refuses to pay for it. [You might think of this as a special use of "won't".]
__________________

won't is even used this way for inanimates,

I should abbreviate it in formal writing?

AnonymousI should abbreviate it in formal writing?

How do you intend to abbreviate it? It's just "won't".

I think he's asking if it's okay to use "won't" in formal writing, instead of "will not."