A second-party developer is a game developer that produces titles solely for one brand of game platform (either Nintendo, Sony or Microsoft). Unlike a subsidiary these companies are in fact private and to some extent take financial risk by opting to (or being contractually obliged to) develop solely for one platform.
Second-party developers are quite rare. A common misconception is that a second-party developer is a wholly-owned (or majority-owned) company - when in fact that definition is the one for a subsidiary.
An example of a second-party developer was Rare who, prior to September 2002, were developing titles exclusively for Nintendo. Nintendo had a 49% stake in the company, and therefore did not have majority ownership. In September 2002 Tim Stamper and Chris Stamper sold their 51% stake in the company to Microsoft, and shortly after Nintendo sold their share as well. Rare subsequently became a subsidiary of Microsoft due to majority (or in this case complete) ownership.
Most developers are either first-party (majority owned subsidiaries or development teams) or third-party (private companies - the majority of the stake is owned privately).
