A third-party vendor is a company that produces software for a platform without endorsement from the producer of the platform.
First-party - software made by the developer of the platform. Example: Microsoft produces IIS to run on Windows.
Second-party - software made by another company under contract from the platform developer. Example: Chess Titans was produced by Oberon Games to be included in Windows Vista.
Third-party - software not contracted by the developer. Example: Sun Java, Apache web server, PuTTy, Bejeweled 2.