I think a better analogy in the US would be universities with an academic focus vs universities with a practical focus. It's not a codified difference and the degrees you get are the same, but it exists somewhat informally.
As an example, in San Diego, the two top universities are UCSD and SDSU. UCSD is much more prestigious but SDSU teaches more practical skills, for example while SDSU biology students have 3 years of laboratory experience, UCSD students will have 2/3rds of one year of laboratory experience. Actually labs will not even consider UCSD students when hiring because they have so little practical knowledge. UCSD students are expected to go on to get professional degrees or higher academic degrees.
In general, in California, "University of California" schools are known to be academic while "California State Universities" are known to be practical. This was somewhat codified in the California Master Plan for Higher Education, where the top eighth of students would go to the UC schools and the top third would go to CSU schools[0].
Maybe the word "equivalent" isn't a perfect fit, but I wouldn't go so far as to say it's "not true." There's some overlap in the concept, if not an exact correlation. I attended a university that had a strong focus on practical applications to the point that it was often tongue-in-cheek referred to as a "glorified trade school."
World Education Services (and others) evaluate foreign degrees and determine the US equivalent, the Central Office for Foreign Education in Germany does the same for US degrees and determines the German equivalent.
The equivalence of credentials matters for example once you get into the realm of government jobs with strict requirements, or getting accepted into Master or PHD programs.
This is not true. Students can get accredited Master's degrees at a University of Applied Science. Some of the Universities even do research.
https://en.m.wikipedia.org/wiki/Fachhochschule
I'm not aware of any trade school in the US where students can get higher credentials than a certificate or associates degree.