Second-party developer
In the video games industry, a second-party developer is a developer who, while being a separate entity from any console manufacturer, is tied to a specific one usually through contract or ownership and makes games specifically for that console manufacturer. Examples:
To be honest, the line between first and second-party developers is a blurry one, the defining characteristic is that second-party developers stand out from the manufacturer, while first-party developers are considered to be more or less a "division" of the console maker itself.