Both Fukayama and Huntington (in the works we're discussing) are products of the reaction to the end of the Cold War. Both wrote the works in question in the late 1980s or early 90s.
Francis Fukayama basically says that the collapse of socialism as prescribed by the Soviet Union took away the last viable alternative to Western-style democracy, in effect ending humanity's 10,000-year search for the ideal political/social system. For Fukayama, in real practical terms democracy is as good as it gets. Yes, people will incrementally be able to make adjustments to democracy here and there and it will always be ripe for reforms but the essential elements of democracy are so applicable and practical for organizing a society that they cannot be improved upon. This is, as one might imagine, a very optimistic viewpoint indeed and it has a Panglossian flavor to it but his arguments about the practical advantages of democracy over all the 19th and 20th century ideologies that claimed they would supercede it are worth reading.
Samuel P. Huntington was specifically reacting to Fukayama when he wrote The Clash of Civilizations. I have been reading Huntington for a long time and think his 1969 work On Changing Societies and his more recent The Third Wave (in which he is much more optimistic than in Clash) were brilliant, but he has a very statist point of view that limits his theories somewhat. Huntington basically says in Clash, "Wait a minute, hold it, hold the celebrations about the end of the Cold War because the collapse of the Soviet-American bipolar world order has unleashed new social and cultural forces that are gonna rock the boat, big-time." Huntington says that a newly-freed world, instead of reaching for ways to strengthen The Global Village through political, social and economic contacts has reverted to its pre-Cold War tribalistic divisiveness, and with a vengeance. The world (according to Huntington) will split into its various ethnic/cultural/religious/regional civilizational components, no one will find anything in common with anyone from another civilization anymore, and the future will be all posturing and warfare.
I disagree with Huntington despite the recent events with 11. September because while in some ways civilizational rifts have indeed flaired, in others they've shrank. While governments have been very slow to react to/with globalism, private citizens and corporations have not and information is flying in all directions across all political boundaries in ways no one could have imagined ten years ago. In his book The Third Wave he talks about how democracy seems to be irresistably spreading around the world; the first wave in the late 18th and 19th century in the English-speaking world and France, in 1918-1945 superficially to other parts of Europe, and the Third in 1989-91 to Eastern Europe, South Korea and parts of Africa. He predicted a Fourth Wave that would engulf the Third World dictatorial holdouts, but in Clash he seems to have decided we're all gonna die anyway.