Very simply put, a 220V unit does not use less electricity than a 110V
unit. It does run more efficiently though than a 110V, which in turn
saves you electricity.

When you pay your electric bill, you pay for watts. The electric
company couldn't care less how much volts or amps you use. It's watts
they are interested in. So now lets compare apples to apples for a
second.
Lets say you have 2 identical 10,000 BTU A/C's. One is 110V rated at 10
amps, while the other is 220V rated at 5 amps ( as a rule of
electricity if you double the voltage , the current will decrease by
half).
Now as the other poster stated. Watts=V*A. So both units in theory use
1.1KW. But because the 110V unit uses 10 amps, there is more of a
voltage drop across the electrical wires from the breaker panel to the
A/C. Resulting in reduced voltage at the outlet, which makes the A/C
run less efficient. But the 220V unit only uses half the amps,
resulting in less voltage drop, less heat across wires, more efficient.
So to answer your question, the 18,000 BTU in all likelyhood does use
more electricity than the 10,000 BTU because it is a bigger unit, not
because it is a 220V unit.