My comment was more about California, specifically, as that's what the original post was about. The state constitution uses the term "full cash value". I dislike the term "Assessed value" because so many people assume it's the same as "appraised value" which is a term that buyers, sellers, lenders, and real estate agents are usually more familiar with. I very much agree with the OP in that I think we should be explicit about the subsidies and/or exemptions that we give instead of hiding them in the way that taxes are assessed.