Third party means that the game is being sold as their own but it was created by a smaller development company. Just because 2 games have the same brand doesnt mean they were programmed by the same people.
Edit: For example all of the BattleField games (battlefield 2, battlefield bad company) are actually made by a company called DICE even though everyone thinks its an EA game.
1st party Nintendo
2nd party Dice
3rd party EA games