I had to dig for this, but I hope it helps (a few years old, but still):
http://■■■■■■■■■■■■■■■■■■■■■/2016/04/the-uc-regents-scholarship/
It looks like the naming of this scholarships is all over the place depending upon which school in the UC system you are looking at. Some schools only have one or the other; others have both.
Other links for the two schools you mention:
UC Santa Cruz: https://financialaid.ucsc.edu/types-of-aid/scholarships/regents.html
UC Riverside: apparently have two
Chancellors:
https://advancementservices.ucr.edu/Scholarship/ScholarshipFundInfo.aspx?fund=01893R
Regents:
https://advancementservices.ucr.edu/Scholarship/ScholarshipFundInfo.aspx?fund=01892R
My D knows Regents at UC Berkeley, some who need financial assistant, some who do not. I think it’s a school’s way of trying to lock down very desirable applicants (GPA, test scores, EC’s) who may be wooed away by other schools. Recipients of one of these scholarships usually receives: financial aid depending upon your ability to pay, or an annual honorarium at minimum; preferencial class registration; guaranteed on-campus housing; access to faculty mentoring; etc. Each school is different.