Like many people you have this idea that an opening is the moves played by one person as if the other person did not exist. The reality is that an opening is defined by both players' moves.
So, for example, the move 1. c4 is the English opening.
If black plays Nf6 we have 1. c4 Nf6, the English Opening, Anglo-Indian Defence.
If black plays e6, we have 1. c4 e6, the English Opening, Agincourt Defence.
So, we have to consider black's move as well as white's second move to define the opening. Here are some examples:
1. c4 Nf6 2. e4 is the English Opening, Achilles-Omega Gambit (because white is giving up the e4 pawn).
1. c4 d5 2. e4 is the English Opening, Scandinavian Defence.
1. c4 e6 2 e4 has actually reached the French Defence, Steiner Variation, by transposition.
1. c4 c5 2. e4 has reached a variation of the Sicilian Opening by transposition.
I hope this makes sense. You need to stop thinking about what you are doing and think more about the moves made by you and your opponent.
white, c4 then e4