Roughly 60 colleges claim to cover 100% of demonstrated financial need for all admitted students.
The distinction between “need-blind” and “need-aware” probably is most significant among those ~60 schools (almost all of which are very selective private schools with very high sticker prices).
About 40 of them also claim to be need-blind in admissions, in addition to claiming to cover 100% of demonstrated need. The schools that are “full need” and also “need-blind” tend to be even more selective than schools that are “full need” but “need-aware”.
https://en.wikipedia.org/wiki/Need-blind_admission
Once a “full need” college decides to accept you (whether through a need-aware or need-blind process) then the amount of need based FA should depend (in theory) only on your demonstrated need, not on your qualifications. Their “need” formulas may differ from some other schools’ formulas, but should apply about equally to all students within that same school’s entering class.
Most other colleges don’t even claim to cover 100% of demonstrated financial need … but most of them also are need-blind. They’ll evaluate your application without regard for need; they may even offer you some need-based aid (or a merit award, or a relatively low sticker price). A need-blind college that doesn’t make the “full need” claim (to meet 100% of demonstrated need on average) may cover up to 100% for some accepted students, but less for others, depending on various factors (such as qualifications, state residency, application timing, etc.)
For any given student, how all these factors play out can be quite complicated. So, it pays to give some thought to your cost-management strategy (and the kinds of reach/match/safety schools you choose to target). Use the online net price calculators to estimate costs for any schools that interest you.