The OP is correct. Any transformer, by design, consists of a primary and secondary winding. You feed the incoming power into the primary winding, and then a new, isolated power source is created on the secondary winding.
This power source then is like a battery.... isolated from the originating power and the earth (since neutral AC is carried though the earth) Just like being able to take a car battery, stand in a puddle, you can touch either terminal (+ or -) (but just ONE of them at a time) and not receive any shock... it's isolated.
The only difference between an "isolation" transformer and a "step-down" transformer is the ratio of loops the secondary winding has to the primary winding. If they are not the same then the voltage will vary accordingly.