Many people think appraisals and assessments are the same thing or at least that they should be for the same amount. The truth is they can vary greatly. Lets look at each of them.
An appraisal is an estimate of market value. An appraiser can use many methods for coming up with this estimate. For income producing property, the appraiser may capitalize the value of the income stream. (It would take x dollars of capital invested at a y rate of return to produce an income equal to the rental income generated by this property.) For other properties, an appraiser may use replacement value. (It would cost x dollars to build this structure if it were being built today.)
Appraisers usually use comparable sales when evaluating the market value of a home. They look at nearby properties with similar characteristics, which have sold in the recent past to see at what price they sold. They typically give the most weight to the property they deem to be most like the property they are appraising.
Buyers and sellers generally encounter appraisals when the buyers lender has an appraiser make an evaluation of the market value of the property being sold. The lender wants to be sure of the value of the collateral for the loan. An interesting feature that comes into play in this situation is that one indication of value is at what price two unrelated parties will agree to buy and sell the same property. In other words, what is the contract price the seller and buyer of this property agreed on (if they are not relatives).
An assessment is the value your local government puts on your property for the purpose of taxing it. How this value is derived varies from jurisdiction to jurisdiction. Some communities say the value is the same as market value. Some say the value is a percentage of market value. Some appear to actually do what they say they do, and some do not.
I was once a partner in an investment property that we were offering for sale at the time the county re-assessed it. Imagine my annoyance when the assessment came in at one hundred and forty percent of the offer price. We weren't dummies. The partners were real estate professionals. I appealed the re-assessment, but my appeal was turned down. I offered to sell the property at the assessed price to the appraiser the county had hired to handle the appeals when he was telling me why he could not reduce our assessment. He did not take me up on my offer. Our property sold at the listed price months later. We had paid six months taxes on the property at a higher than market value.
On another occasion I helped some elderly people sell a farm they'd lived in all their adult lives. The farm sold for a price a great deal higher than the value at which it had been assessed.
I believe the two examples are fairly typical. Many jurisdictions will puff up assessments for businesses and investors and low ball assessments for people who have lived in their homes for a long time. Sometimes there are formulas for doing this. Land use is one such concept, i.e., the property is taxed at its value as a farm and the fact that it is ripe for dense residential and commercial development is ignored or deferred. Sometimes there are no formulas. It is just done.
For these reasons, it is usually not a good idea to put too much credence in the assessed value of a property when you are trying to figure out market value. They may be the same. They may be vastly different.