In short
Look up if you are overpaying.
Is a board of equalization the same as the assessor?
No. The IAAO glossary lists Board of Equalization as one alias for an assessment review board, a quasi-judicial panel that hears assessment and classification matters. Board of Assessment Appeals and Appraisal Review Board appear on that same list. The naming is local. The job is the same: a seat that is not the assessor's office, opened after a formal filing. This page is not a filing guide.
What does a board of equalization do on a tax appeal?
It is the room where a formal property tax appeal is heard. An informal talk with the assessor, if the county offers one, is a different room. The informal versus formal page keeps those two apart. FairAppeal handles the entire appeal on your behalf when a case is filed. The Fair Appeal appearance is the point of hiring the service: the homeowner is not the person arguing in that room.
Related reading: the property tax glossary and what a property tax appeal is.