These rules have to do with employer HSA contributions.
The comparability rules say that an employer can only vary contributions based on a few factors, like self-only vs. family coverage or union vs. non-union employees. Essentially, similarly-situated individuals have to be treated the same.
In general, the comparability rules do not apply to HSA contributions, though, since most groups that allow for HSA contributions through payroll will have a 125 plan in place. In that case, the non-discrimination rules (which say an employer cannot discriminate in favor of highly compensated employees) apply. There is not a separate non-discrimination test just for the HSA contribution, though; it’s combined with the other benefits for non-discrimination testing purposes.