New York, separate contracts
Somewhere in my brain, I do recall that we were told when we purchased several years ago that NY membership had to be purchased through Hilton.
Advantage: with the NY purchase, which is only for 25-30 yrs, you do receive Hilton Gold membership. You can trade into any other property (reverse isn't true) AND, when you are gone and can no longer use the property, your heirs won't inherit it or its maintenance fees. They won't feel they have to keep it and pay the fees . . . 'cause it just isn't there.