Moving an object implies different things depending on the object you're trying to move.
Pick Up - the character takes the object with their hand, picking it up, and carries it with them.
Grab - the character grabs hold of the object with 1 or more hands, to pull/push or even strangle.
More accurately it depends on the size of the object you're trying to move.
So how do we decide when to pick up and when to drag? We check the number of available hands..
small objects - always pick up
medium objects + one free hand - drag
medium objects + two free hands - pick up
large objects - always drag