I believe our district uses an initial option where you're serviced based on either high achievement or high aptitude (but they only do the CogAT in 3rd, so after that it's really all achievement-based).
Some kids are supposed to be flagged with a matrix (of CogAT and high achievement on state test) to catch some who do better on one than the other. A few who aren't offered services for 4th grade are later added in based on state test and MAP scores (or grades in honors classes) in future years.
At the core, though, it's achievement-based, and it varies in program approach. Literacy is differentiated within classes, with GT coordinator support on the side, assisting the teacher with enrichment, up until AP classes. All kids are required to take the same core curriculum until 11th grade (when AP kicks in), with elective options on the side.
Secondary honors science apparently uses the increased rigor & depth approach, and requires high achievement for acceptance.
For math, there's no compacting of 2 years of earlier grade math, and the advanced math path is only honors in name (it's the same year-long course, just ahead of age-grade), not offering an increased pace/compacting while going deep and wide on less typical content, which I find disappointing, after all I've learned about taking math to the next level in mathematical thinking.
I get the sense that the schools like to have hard achievement test numbers to justify why kids are given the challenging path, rather than going by cognitive ability and thereby affording challenge to the under-achieving kids who haven't been demonstrating what the school expects. If you go by ability, then you have to offer more testing, and it's harder to explain to some people why A got in and B did not.
