Honors and Advanced can certainly mean very different things to different schools. From what I understand, colleges often totally disregard any designation other than AP or IB.
At my daughter�s school (top quartile students), all courses are considered a minimum of �honors level� with additional Advanced designation for some math courses.
My son�s school takes a wider range of students, so they offer at least three levels for every math course with �honors� being the highest. They do a great job of maintaining the rigor though as they only accepted a dozen students (half are international students) for his current honors geometry.
