The market is real and dynamic, a negotiation between what the buyer and the seller think a property is worth. Either side can reject the offer if it's not satisfactory. The sale price of a home reflects the current market and the assessors will get around to it eventually. Because there can be error and because government in terms of housing is not trying to be ruthless, a locality might have a percentage of value used for assessment. You have to research each locality to know, it's usually not clearly stated.
The sale price of a home is based on what the market is doing right now. That's why some houses, particularly in the DC area, are now selling for higher than list price, because inventory is low and demand is high in some areas.