I consider these economic categories, primarily.
You are middle class if your income is fairly median, you probably work for someone else though you might have a small business, you will though have access to things like pensions or some investments for the future.
There are things you can associate with this - for rxample most middle class people can reasonably expect their kids might go to university and it's fairly likely that they might have gone themselves, but that's more a correlation than definitive.
It's also a bit confusing that lots of jobs that used to be working class are now more like middle class jobs because of the pay and benefits associated with them - trades jobs in particular, certain military jobs, that kind of thing.
As a kind of quick imperfect heuristic, I tend to think of the difference now between a working class and middle class person to be whether they have access to investments and pensions or similar ways of growing their money, at least to take care of their retirement.
The cultural elements of class, like values, the sports we like, and so on, can come as much from our parents' class as our own. So since as a society we have a lot more class movement than some others, especially in the past, it's pretty common to get people who may themselves inhabit a particular class but their cultural roots are in another.
For example, in my grandparents generation, I have examples of that in two directions. My paternal grandparents grew up very working class, and for years were themselves working class, but later moved into the middle class - which was not unusual at that period of time as many families were increasing their standard of living. Their culture remained very working class, as did that of their kids who were older by the time they moved up. My maternal grandmother on the other hand grew up as a quite posh until her early teen years, but her family became poor after her father died - enough so that she had to quit school early and go out to work. But her values her whole life remained much more shaped by the earlier family culture even though she married into a very middle class family.