There's an interesting difference in The Picture of Dorian Gray between these two terms, "art" and "culture." While we might normally view them as two part of the same whole, Wilde asks us to examine them more like two sides of a coin here – they're inextricable, but not identical. According to Wilde, art is a good thing; it's purpose is to be purposeless, and the only thing it should be is beautiful. Culture, on the other hand, is not necessarily a good thing – it can be a bad influence. Dorian Gray examines the weird gray area (pun very much intended) between the beauty of art and the fascinating corruption of culture.
The conflict between Basil and Henry essentially represents the difference between "art" and "culture."
Dorian's immediate one-to-one identification with the portrait demonstrates his failure to understand real art, which, as we see in the Preface, is meant to be purposeless.