May vary some state to state, but here the assessment process goes something like this:
Auditor (Town Assessor for us) collects home sales data for a year. Then spends a year building and tuning the assessment model, and then getting it certified by the state. Then you get a new assessment, which is about 2 years out of date. When prices are going up you feel good, because it is a low number and you think you are getting a deal on your property taxes. In a declining market the number is high and you feel screwed.
On average since these biases are shared by everyone it really does not matter.
But assessments even if done pretty well are never really for your property. Only rarely does a house get visited and the actual value of sprucing up, landscaping, or negative value of not keeping things up come into play.
So unless values are pretty flat, and you live in a very average house, will assessments match up closely with an appraisal.
What matters in most cases is a true assessment. Of course those can be less than perfect as well. No one knows the value of their house until they make an honest attempt to sell.
Best of luck.
We live a world with knowledge of the future markets has less than one significant figure. And people will still and always demand answers to three significant digits.