You don’t even need an industrial PhD. In Denmark at least, a PhD study is a paid position, essentially just a job that runs 3 years and results in handing in a PhD dissertation. It pays less than what you get in the industry, but very decently, so no need to balance multiple jobs, just focus on your research.

The Industrial PhD pays the same here, so that’s mostly a position you would take if you specifically want to collaborate with a company on some research project, not something you do because of income considerations.

Yup, that's correct.

Maybe it depends on the field and the country, but I know some industrial PhD position pays a better salary than the one employed full time by the university. Not sure if it is considered to be "much", but at least around 20% more.

I would add a word of warning here. In the multiple research groups that I've worked in, the completion rate for industrial PhD students has been way less than 50%.

The industry part (whether 20% or 50%) easily ends up being close to 100% in practice. And many industrial PhD positions only last a few years, after which you get a normal full-time position and are expected to finish the PhD on your free time. Realistically, this makes it practically impossible to conduct the kind of research that you need to get a PhD from top programs.