My understanding is that it's more about where people get their wealth and income. Working class primarily gets it from labour. Middle class has a mix of capital and labour income. And upper class / capitalists get it mostly from capital.

Degrees and jobs align with those but don't define them, as far as I understand it.

Then again in my mind the only distinction worth a damn is "contributor" and "parasite" and so we're all working class and we should see ourselves as aligned against the individuals and families who have enough wealth that generations of them will never need to work a day in their lives.