Some people mistakenly believed that assessment is the same as appraisal, including my neighbor who came by the other day. He thinks that assessment is appraisal. It is not. It's two different thing. Assessment is what the local government assess of the value of a property based on a formula - for tax purposes. It could be mass appraisal, not independent appraisal, like when you want to get financing from your lender. You get to how much your house is worth, usually after an appraiser is sent out to preview your house, at the request of a lender. If you are selling, lender put the order on behalf of buyer. Based on what the appraiser sees (including improvements), recent comps, the appraisal would then give his/her professional opinion on the value of that property (either use for financing or refinancing).
Though, if we look at the example below, Arlington County's formula for tax assessment is directly linked with how much the house would sell. Assessments are made at 100% of value. However, for some other jurisdictions, like the District of Columbia, it is a different story. DC uses a different formula than Arlington. They use what they call the 'assessment ratio,' which is the assessed value/ sale price ratio. To me, DC's formula it's kind of complicated to figure it out. There's so many different average variations they use. (You can read here for more). The assessment ratio is then used to get to the estimated fair market value.
Here's my interpretation..Assessment vs. Appraisal
Resources:Arlington County Real Estate Assessments