I had to whittle your question down.
Civilization can be used to represent a broad concept of culture, but there are differences. Civilization can refer to the process and effect of urbanization, industrial development, technological advance and expanding in complexity in all phases of life. Being civil can mean to be polite especially in a formal way. There is also an inference that civilized societies (more technologically advanced, namely Western and European) are more civil (in this sense) and thereby more refined and enlightened than more primitive cultures. However, recent studies in postcolonialism and criticisms of Eurocentric ways of thinking are quick to point out that being civilized (as in industrialized) does imply that their way of life is morally or ethically superior to the more primitive (so-called ‘third world’ or even ‘barbaric’) nations and countries. So, civilization is a nuanced term and depending on who uses it, can refer to enlightened or just technologically progressive.
Civilization is a broad term and different cultures or examples of culture could be thought of as subtitles of certain civilizations. For example, during the American Civilization there have been many cultural shifts. Two large social shifts which affected American culture and helped redefine it were WWII and the Civil Rights Movement of the 1960s. In this sense, American Civilization is the general progress and history of America and also how that history has helped shape culture.
Culture can mean the elite or accepted (by a select group or majority) as the best art and literature. Culture can also mean a broader concept: the attitudes, beliefs, ideologies and actual physical practices of everyday life in a certain group of people. And this group could be called a civilization or a culture. Remember that American culture is the culture of America at a given time or within a particular context or discipline. Examples: American Yuppie Culture of the 1980s or the Indie Rock Culture of Austin, Texas.
Similar to being civilized, being cultured initially referred to enlightened people with a particular reference to high art. Over time, high art, the concept of elitist culture, the concepts of civilized and primitive (and Eurocentrism) all began to be challenged and deconstructed. The sense of enlightened thought and refined art still exists, but motivations for valuing art and judging civilizations has become much more ‘culturally’ responsible.
You might say that the culture of a certain people at a certain time (and sometimes in certain social groups like democrats or hip-hop artists) represents the beliefs, practices and social interactions of the people of those respective groups. Many cultures make up the totality and history of a civilization.