Misplaced means you have the possibility of finding it–it’s somewhere that you can access but don’t know where it is.

Abandoned means that the person willingly gave it up and may or may not know where it is, but got rid of it intentionally.

Intent is judged by an objective standard.

Something, like an old chair, thrown into the trash is typically abandoned, whereas a dollar bill on the street is typically lost (since people don’t typically abandon money).

If its by the curb with no one near by, it’s abandoned and it’s okay to to take it.

If he loaned me something and I can’t find it when he wants it back, I lost it and I owe him for it.

If he had it and he can’t find it, he simply misplaced it.

Don’t know where it is/Unable to find it

Misplaced

Don’t know where you left it/but you remember a general area

Abandon

Don’t want it anymore/just left it