If you are going to commit to living in a tiny house, I would definitely advise you to do a ton of research. I did it on an impulse as a quick fix and haven't had the most ideal experience.
Like I said before, knowing what I do now, I wouldn't be opposed to living tiny again, if the conditions and circumstances were right.
As to your observation about a tiny house being close in size to a one bedroom or studio apartment, in my case I would say they are both much larger, at least in my area and in comparison to the size of my shack (9'x13'). It could also be that the layout of these types of apartments make them seem larger than they truly are but I'm not sure.
As far as space constraints, to live in a tiny house right, the best way is to be a minimalist. I will say that though I wouldn't classify myself as a minimalist, living tiny has taught me about excesses, and enjoying life with less. I'm often shocked now at the size of people's average homes and the amount of decorations and stuff they fill them with! When you don't have a lot of area to fill and decorate, you naturally become more thoughtful about what should and can go here or there.
Thanks for sharing @theb0red1! That minimalism is what attracted me to tiny houses in the first place. With the restrictions of the space, you really have to think about what you really want and need at the same time.
Still, you are right. There should be a ton of research to be done when deciding to move into a tiny house. In my case, here in Asia, condos are just about the same size (in floor area) or smaller than tiny houses and they cost A LOT! I reckon if I'm going to be spending as much money, I might as well build it in a more practical manner. Thus, the tiny houses.
Still not sure how this could be applied in my location, but I'm looking at options. :)