No, it doesn't mean the same thing. We are apples and oranges. Even on Mudcat we've often discussed how language in the UK and the US is different, and the way we use the word "middle class" is an example.

We are supposed to be a classless society. But instead of middle income, people have the habit of saying middle class. The label does not even have a clear definition.

This quote is from the Wikipedia page on "American middle class".

"Everyone wants to believe they are middle class...But this eagerness...has led the definition to be stretched like a bungee cord — used to defend/attack/describe everything...The Drum Major Institute...places the range for middle class at individuals making between $25,000 and $100,000 a year. Ah yes, there's a group of people bound to run into each other while house-hunting.
—Dante Chinn"
http://en.wikipedia.org/wiki/American_middle_class