I think there are differences. If you have a few, like 4 or 5 that you change out and they were given as gifts and that sort of thing, I don't think you are a collector. Even if you bought all of them for yourself just so you have some variety for your wardrobe. Once it gets to a point where you are buying and selling to make room for new ones, even if you only have 4 or 5, then you are a collector.
If you look at classic cars, if you bought yourself 1 classic car and that is all you have, you are a collector. If your dad had a classic car and passes it down to you, people could say you are a collector, but in that situation I don't know that you are as you didn't go out and buy what you wanted. It is more sentimental at that point, where the one you purchased, could be sold for a different one that suits your tastes later. The same could be said about the one passed down, but that would make you a car collector then.