No, you buy direct from Amazon or from 3rd-party sellers. These sellers can store and ship by themselves, or pay to have it stored and shipped by Amazon (this is called FBA - Fulfilled by Amazon) because it's faster and qualifies immediately for Prime which customers want.

You can tell the difference when you buy, it's just not blatantly obviously unless the main Amazon listing is out of stock and you click on the "other sellers" link yourself. Go to your orders page and every product will tell you the "sold by" name.