Why are working class whites so often defined as "whites without a degree?"

[TheDeadFlagBlues]

A contractor or self-employed tradesperson is petty bourgeoisie.

Maybe from a theoretical perspective but, in practice, that's not correct. There's a very big overlap between small-time contractors, much less self-employed tradespeople, and those who are employed by contractors as skilled workers. I know this because my grandpa was a contractor and my dad is a self-employed tradesman. Both worked for contractors themselves, sought representation from unions when they did so etc. Neither of them have/had a self-conception as a "business man" or even a "business owner".

Being a self-employed tradesman is very attractive to building trades workers because the field is dangerous and physically draining, defined by unfair practices; most workers desire more autonomy over their own work. Because unions only cover major public works projects these days, becoming self-employed is the only way to obtain a modicum of security on the job.

History can also explain this. The building trades are unique in that they are pre-industrial professions/occupations. Historically, artisans in the building trades had autonomy and effectively were self-employed but advances in building technology and changes in the labor market eroded this autonomy. However, the traditions remain and, to this day, even road construction workers take pride in "owning" their tools.

[TheDeadFlagBlues]

"Working class" is a separate class from "blue collar"?

Well, there are blue collar people that are actually quite wealthy now. Tradies, for example.

Wealthy tradespeople are generally small business owners not those working for someone else.  It also strikes me as strange that the term blue collar = just the "royalty" of the blue collar world.

Often you wouldn't actually define - at least if you're from the social group in question! - a man who runs a little building firm that employs a handful of people a tradesman anyway of course...

Yep and the reason can boiled down as follows: for workers in the trades, what makes someone a "workingman" or a "tradesman" is whether or not that man works with their hands. Plenty of small-time contractors do most of the tasks of their employees. In the US, it appears that this isn't common anymore and that most contractors see themselves as people seeking returns but the tradition still exists.