ChatGPT has for sure the "first mover" strength for normies (you can hear it mentioned in TV, radio and in the street, but also lot of people just talk about "AI". So, IMO there is still space to be used as "the AI" rather then specifically ChatGPT. It might also just be always referred to "ChatGPT" when talking about another provider, just like people saying "Kleenex" when referring to tissues.