Manlytears said:
It's a somewhat controversial topic, which is why it generates confusion among people; however, the classic notion of "first party" is that the studio (developer) belongs to the publisher.
I recall seeing statements from Microsoft that they always considered games published by them as first-party, regardless of who made them. This kind of confusion is understandable, however I reinforce the classic notion that first-party is when the studio belongs to the publisher.
I believe the most notorious examples are pokemon games like “Red”. It's not first party game, it's a second party exclusive, made by Game freak ( studio not owned by Nintendo), published by Nintendo and IP owned by 3 companies.
It's similar with OG Demon's Souls. It's made by From Software, published by Atlus (America), IP owned by Playstation.
By your standards OG Demon's Souls would be Atlus (now SEGA) third party exclusive game. But the game is published by Sony in JP, so... Kinda confusing, publisher can change depending on region.
The notion of "publishing = 1° party" can cause some major confusion. For exemple, Call of Duty: Black Ops 4 is not Playstation 1° party, but it is published by Sony in Japan.

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