The difference is that regular or classic cheesecake is made with heavy cream and sour cream to be a little tangier and creamier. A New York cheesecake is all about the cream cheese which makes it so dense. I prefer a combo of the two, cream cheese for heaviness and taste and sour cream for a bit of tang and to smooth the filling out a bit. You may also have heard of a Philadelphia cheesecake. That's a cheesecake made with cream cheese, or more specifically, Philadelphia cream cheese and is a marketing ploy by the Philadelphia cream cheese people to make more money. They can be used interchangeably.