The bit about two-way mirrors reflecting off the front side instead of the back is an "urban myth." They're made just like a regular mirror, but with a thinner layer of the reflecting (once silver, but now often aluminum) layer.

The way to tell if they are two-way is to turn off all the light on your side, and then (only) if there's any light on the other side it will show through. They work both ways, but the "through" image is hidden by what's reflected if you're on the side that's more brightly lit. (And if you're on the other side, be careful not to turn on the lights.)

And probably the reason you feel that you look "different" is that most "fitting rooms" have at least two mirrors, at an angle to each other so that you can see your backside (if you want). You tend to see yourself from several sides at once, and from different directions than your used to. (Is it cruel to say that's the way you always look to other folk?)

John