As to the topic of the thread (sorry about that detour I had to take in the above post), culture is a complex, multi-layered concept. It is, after all, more organic than dictated by national or provincial borders.
There are sub-cultures within cultures, old hereditary allegiances within new lands which are usually quite strong at first (recent immigrants to the US are often illustrative of this) and diminish, but may still have SOME significance, over time (second, third, fourth etc. -generation Americans--still keep a few traditions, but have also fully assimilated), and local traditions that coexist with broader ones. One could say his family, in some ways, has a distinct "culture"--ideosyncracies and such that THEY understand but others may not--it all depends on what "layer" of culture you are talking about.
That said, in a rather "broad-layered" sense the US DOES have many distinctions with Europe in terms of culture. This was starting to occur even in the colonial days--European colonists in America had to adapt to the conditions of the new land, the presence of the indigenous people, unfamiliar or more prevalent wild animals, a colonial type of economy, and other things that were different from the well-known, well-established, and well-worn lands in Europe. Of course they would evolve a different culture to adapt to their new circumstances. They developed a "frontier" culture, and many aspects of this exist to this day even though the US is hardly a "frontier" anymore. But that is just one layer. There is also the American commercialist culture, which some would say is being exported excessively everywhere else--but if you've ever been to Japan like I have, for example, you would see that while the Japanese have imported much of this and assimilated it, it is just on the surface and beneath that surface, the people are still very much Japanese and very different in many ways and attitudes from Americans. Again, we are talking about a complex, multi-layered phenomenon. And one that is not easy to define, even for anthropologists, who are the professionals in this area.