No - most middle class people also have to wrok for a living. If you don't have to work for a living, then you are probably landed gentry and therefroe upper middle class.
It's somewhat dated now, as "class" today seems to be more to do with aspirations and epxectations, but "middle class" used to be more to do with the professions and being comfortably well off, porbably home owners while "working" class was more blue collar/manual work (yes, and probably included working in a shop! ) and without much income and probably renting.
Those are very much borad brush generalisations!
In many cases, a "middle class" family porbably had less disposable income than a "working class" one, as they had mortgaged themselves up to the hilt in order to buy a house/send children to private schools/have fancy holidays!
Now everyone wants to own their homes and we all go aborad for our holidays!
For the record, I owuld consider myslef to have been brought up "middle class" - my dad's a doctor and my mum's a teacher, but when I was young, we really struggled for money as they were students paying thier own way. My dad had been a farmer, so did have some money from selling that.
My dh would probably say he was from working class stock - his dad was a BT engineer and his mum was a primary school head teacher.
What was probably more signficiant in our perceptions of relative class was where we were brought up: I was brought up in a middle class (snobbish) suburb and dh was brought up in a much "poorer" (in money terms) environemnt - although it was probably far richer in terms of sense of community.