With a lense, it is a convex lense that magnifies. That is the lense that is fatter in the middle and thinner on the edges. The classic magnifying glass.
With a mirror, it is a concave mirror that magnifies. It is not depending on the index of refraction from a lense, so it works differently.
To test this simply, grab a shiny spoon. If you look into the bowl of the spoon, at the correct distance, your eye will be magnified, but distorted because the spoon's bowl is not round but rather more egg shaped. If you look at the back side of the bowl or on the outside of the bottom of it, things will look rather smaller.
http://regentsprep.org/Regents/physics/phys09/breflconc/