The Guardian Units of Nations is an international peacekeeping organisation in Sonic's World.
G.U.N was heavily involved in events on the Space Colony ARK, especially the forced cancellation of Project Shadow. Their presence is felt in games throughout the Sonic series, which include locations apparently within United Federation, but also many that appear far removed from it.
There is some ambiguity regardng G.U.N's nature geopolitically. In terms of real-world parallels, it seems closest to a millitarised United Nations. It's presence seems to be stronger in the United Federation than in some other nations, but assuming that it is the national defense force of that country raises contradictions - as noted above, G.U.N appears to have a more worldwide presence than any individual country's military would be expected to. Their heightened presence in the U.F. could be due to close ties that it has with the founding and funding of G.U.N, or it could also be that many perilous world events have been localised to apparently American-inspired (read: United Federation) locations.1 At any rate, the name 'of Nations' invariably points to an international organisation (or, possibly, a multinational weapons manufacturer??).
G.U.N's intervention in the United Federation funded research aboard the ARK half a century ago could be interpreted either way; a forced shutdown by the government that funded it, or external intervention by a regulatory body. The truth could be in a more grey area; that the U.F. requested G.U.N aid, or that G.U.N also had fingers in the Project Shadow pie; it is all admittedly rather muddy, and doubtless just a plot oversight caused by SA2's rushed development.
In saying this, the worldwide presence of GUN seems to have tapered off, with the last reference to the organisation in Sonic Frontiers, a throwaway line, being the first reference to it again in a Sonic game in... I wanna say nearly a decade? No reference was made to G.U.N at all during the worldwide upheaval depicted in Sonic Forces either. However to speculate as to why would push this firmly into the Fanon category.
The geopolitics of Sonic's World are, of course, largely undetailed and can only be guessed at, but given the existing real-world parallels, this interpretation of G.U.N seems reasonable.