Perhaps. I'll clarify:
In a 2-player game in which players alternate taking turns, "player order" means "who goes first". "Changing the first player" is essentially synonymous with "changing the player order.", because there is no "player order" in a 2-player game (other than deciding who goes first).
In a 3-player game, that is not the case. ABCABC etc and BCABCABCA has a different player going first, but the sequence in which the three players take their turns remains the same. B Follows A. C Follows B. We could also have ACBACB etc. The same player is going first, but the sequence has changed.
In a 2-player game it makes no sense to say, "the first player changed but otherwise the turn order remained the same."
In a 2-player game in which players alternate taking turns, "player order" means "who goes first". "Changing the first player" is essentially synonymous with "changing the player order.", because there is no "player order" in a 2-player game (other than deciding who goes first).
In a 3-player game, that is not the case. ABCABC etc and BCABCABCA has a different player going first, but the sequence in which the three players take their turns remains the same. B Follows A. C Follows B. We could also have ACBACB etc. The same player is going first, but the sequence has changed.
In a 2-player game it makes no sense to say, "the first player changed but otherwise the turn order remained the same."