I endorse polarbear's position. Sussing this out requires direct conversations with the individual schools. There are some standards around the AP label, but what does "Honors" mean to them?
In my school, "Honors" was a label that was affixed to any top-level class that didn't have a connection to an AP test. There was an Honors Algebra II class because The College Board doesn't offer an AP test for that subject, but they do for US History, so advanced students wanted APUSH. There was no either/or, they were simply the labels you looked for if you were an advanced student and wanted the most challenging version of your courses. Whether anyone actually took the AP test at the end of an AP course was entirely at student/parent discretion.
