He said one socket, which means 55Watts.

He could have meant one ballast and just used the wrong terminology.

So, to clear it up, here is the one vital question: How many bulbs light
up when you turn on the power?

If two do and you bought the 2x55W system, then you have 110W. If only one
does, then you have 55W. The 2x55W system means they send you one ballast
that drives two 55W bulbs. They have other "2x" systems as well. I for
example have a 2x36W system.

This is confusing, in a way....

One ballast, and two lights, that plug into one square 4 pin socket. 1
socket, 4 pins, 2 light tubes...

I'm as confused as I thought I was.... or am.... or will be.... confused
that is....