If N makes and publishes the game, thats 1st party.
If N only publishes the game and some other company is in someway owned by Nintendo makes it, thats a 2nd party game.
Second party is where the company gives the project to a wholly owned subsidiary, i.e. a separate corporate entity that could in theory split and join another company, example: Bungie under MS, Rare, Monolith Soft.
Careful. If a company is WHOLLY owned by a first party, they are part of the first party. If the first party owns at least 51% of a company, they control that company, and it is first party.
Bungie was wholly owned by Microsoft. They had no power to break away from MS on their own; MS let them buy themselves back.
Rare was independant from Nintendo. N owned 49% of Rare, and Rare's founders owned the other 51%. Microsoft bought the 51% first, and then Nintendo sold the other 49%. So Rare was "second party" to Nintendo, and are now first party to Microsoft.
"[Our former customers] are unable to find software which they WANT to play."
"The way to solve this problem lies in how to communicate what kind of games [they CAN play]."
Satoru Iwata, Nintendo President. Only slightly paraphrased.
