The purpose of he game capture source is to grab the video frames from a directx-based or opengl-based 3D application. Usually, this is how games are captured best. If a game or application does not use directx, it cannot be captured by game capture, but probably by some other source type.
The Window Source grabs one specific Window from your desktop. If a game runs windowed, you can probably grab it with either the game capture source or the window source, but using game capture is more efficient.
On laptops, it might be difficult to get an application (game or normal app) with game capture or window capture. Game capture does not always work, even if the game is directx-based. In this case you can use display capture as last resort.
Display capture is similar to an external capture card, if you use it to "capture yourself" and not a second device, but it is more efficient than a capture card. See it as emulation of a capture card that is free and more efficient than a capture card.