Do I have to follow the openings moves when the response is different? This question concerns the opening. For example, in the Danish gambit:

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1. e4 e5 2. d4 exd4 3. c3 dxc3 4. Bc4 cxb2 5. Bxb2


white reaches the desired position. But what happens if the opponent deviates from this move order? Would it still be the Danish gambit? Can I still follow the moves in the Danish gambit or do I have to use other moves? Does an opening variation involve any alternative moves?
You never "have" to follow an opening sequence, especially just for the sake of following an opening name. There's nothing special about the "Danish Gambit"; it's just a group of moves someone decided to give a name. Any sequence of moves can be given a name if people really wanted.  If your opponent plays a different move order or unexpected move you should adjust your play accordingly. But of course there's always a chance you might transpose back into that "Danish Gambit" line depending on what moves are played.