These are three terms that can cover what I'm doing, but I've also seen enough debates of what one is calling this hobby that it is clear that some people find it important to distinguish them from each other.
Personally I'm calling myself a costumer. For me it's the crafting of the costume and the wearing of the costume that is the important thing. I am the kind of costumer that likes pretty things, and I love the chance of being able to wear corsets, big skirts, silks and velvets. This also means that I enjoy making the costume, almost as much as I enjoy wearing it. This is of course also the reason why I'm not satisfied with just one costume, but wants to just continue with a new project as soon as I've finished a costume.
I do not consider myself a cosplayer. I've seen quite derogatory remarks from costumers towards cosplayers, and don't agree with that. The reason why I'm not calling myself a cosplayer is simply because I don't consider myself a good actor. I definitely have a problem stepping into a role, and become a certain character. I really admire cosplayers that "are" the character they are portraying. Now sometimes, especially when it comes to my SW costuming, I definitely do cosplay.
I'm not an historical recreator either. I think it's great that you have people who are really into showing history as it really was, and trying to recreate all the details of the past. Even though I research my historical costumes as thoroughly as possible, and try to get more and more accurate with my techniques, I don't mind using a sewing machine for sewing long seams. Once again just like with cosplay I'm not into getting a persona and trying to recreate the behaviour of people in the past, I just want the pretty clothes.
If you call me a cosplayer I'm really fine with it, and if you call me an historical recreator I will be very flattered, but costuming is what I call my hobby. Costuming is also good since it covers everything, from history to the future, films and fantasy.