My diploma states the type of Honors degree I earned- one can do honors in the major, comprehensive honors and another variation. This also meant the “with honors” information would be part of info on my degree sent out by UW. Of course, by now that is ancient history for me. It was more than just the H after the grade on the transcript for many courses.
One can make use of an Honors Program take honors courses but to get the degree one needs to meet depth, breadth and grades criteria. So I do have a different diploma than the regular one. btw- UW dropped the magna. summa et al cum laude designations because honors implies more rigor.
One needs to not only evaluate the total costs of being in an honors college/program but the courses available. Some seem to be for the first two years while others include a means of honors in various majors et al. Some schools will give merit money while others do not.