Since no one seems to have complicated this further by mentioning
another kind of transformer, let me do so. I may save someone a
nasty shock in the process.
There is a kind of variable transformer called a "Variac". The
Variac also delivers a stepped down or stepped up AC voltage, but
it has only one inductor which is tapped at an intermediate point
and equipped with an adjustable tap attached to a big knob. This
object is a variant of a beast more properly called an
"autotransformer". Unlike a real transformer, an autotransformer
shares a common connection between primary and secondary. It is a
three terminal device, but it is dressed up to conceal that fact
in the case of the Variac. A nasty shock can result if it is used
carelessly, expecting that primary and secondary are insulated
from one another.
If you have one of these around you should learn exactly how it
works before you use it, and you should probably not let high
school students use one at all in any application in which it is
not prewired into the circuit in which it is being used.
You may guess that I learned my lesson with Variacs the hard way.
You would be right. I didn't get a shock (I barely notice 110 VAC
shocks anyway), but I did arcweld a nice hole in the grounding
lug of a signal generator in the process. The Variac is a useful
device, but it should be used with intelligent caution.