The Laughing God is an Eldar God. It was he who tricked the Outsider into eating other C'tan. Those Eldar who follow him, known as the Harlequins, are protected from Slaanesh in a different way from their Craftworld brethren. While Craftworld Eldar wear Spirit Stones which absorb their souls when they die, Harlequins are directly protected by their God, becoming one with him on death. The only exception to this is the Solitaire whose soul must be won from Slaanesh by the Laughing God.
The Laughing God should not be confused with the Deceiver. There are a pair of stories about the Laughing God and the Deceiver respectively which cause this confusion. In one, the Laughing God tricks the Outsider into eating many other C'tan, driving him insane. In the other, the Deceiver consumed several C'tan to increase his own power and convinced the Nightbringer and the Void Dragon to do likewise. Neither of these C'tan, nor the Deceiver, were driven insane; obviously a significant difference.
Perhaps most significant however is the obvious difference between the origins of the Laughing God and the Deceiver. The Laughing God was created by the belief of the Eldar, in the same way as were Kaela Mensha Khaine, Isha and the other Eldar Gods, and as such is a warp entity. This is supported by his ability to compete for Eldar souls with Slaanesh. The Deceiver however is a C'tan, the soul of a sun, an entirely material being. The mysteries of the Immaterium are beyond the C'tan, who find the Warp an entirely uninhabitable place. How then could the Deceiver fulfill the role ascribed to the Laughing God?