Push the door open.
‘open’ is complement. It description the OBJECT(door).
Push the door hard.
‘hard’ is adverbial. It description the Verb(push)
In most situation, not all situation:
Complement only have relationship with Noun.Adverb only have relationship with Verb.
I played football happy.
‘happy’ is complement.
I played football happily.
‘happily’ is adverbial.
I played football yesterday. / I played football on the square.
‘yesterday and on the square’ art adverbial.