The United Earth Government or the UEG is the central civilian government for Earth and the innermost colonies. The UEG houses the Colonial Administration Authority, and therefore the UNSC.
Differences Between the UEG and UNSC
The UNSC is the exploratory, scientific, and military arm of the human government. The UEG is resonsibile only for Earth and the colonies, the main locations of human government. The UEG would house the executive, legislative, and judicial branches of government, leaving defense mostly the responsiblity of the UNSC. It may act as a sort of United Nations, bringing Earth nations together into a unified government.
UEG Military
The UEG Military is the UNSC
Marathon
It should be noted that both the UEG and UESC are references to the human government and military in the early Bungie game, Marathon. See List of Marathon references in Halo.