Many people think that appraisals and assessments are the same thing, or at least that they should be for the same amount. In fact, they can be very different. Let's take a look at each one.
Appraisals
An appraisal is a guess of the value on the market. An appraiser can come up with this estimate in a lot of different ways. For properties that bring in money, the appraiser may put the value of the income stream into capital. (It would take "x" dollars invested at a "y" rate of return to make the same amount of money as this property's rental income.) "Replacement value" may be used for other kinds of property. (If this building were being built today, it would cost "x" dollars to do so.)
Most of the time, appraisers use "comparable sales" to figure out how much a home is worth on the market. They look at nearby properties that have sold recently and have similar features to see how much they sold for. Most of the time, they give the most weight to the property they think is most similar to the one they are valuing.
Appraisals are usually done when the buyer's lender asks an appraiser to figure out how much the property being sold is worth on the market. The lender wants to know for sure how much the loan's collateral is worth. One interesting thing about this situation is that the price at which two people who don't know each other will agree to buy and sell the same property is one sign of its value. In other words, what is the agreed-upon price between the seller and buyer of this property? (if they are not relatives).
Assessments
An assessment is how much your local government thinks your property is worth for tax purposes. How this value is found varies from one place to another. Some people say that the value is the same as the value on the market. Some people say that the value is a share of the market value. Some of them seem to do what they say they do, while others don't.
I used to be a partner in a rental property that we were trying to sell when the county changed its value. Imagine how annoyed I was when the assessment came back at 140% of the offer price. We weren't dummies. The partners were people who worked in real estate. I tried to get the reassessment changed, but my request was denied. The county hired an appraiser to handle appeals, and when he told me why he couldn't lower our assessment, I told him I would buy the property at the assessed price. He did not accept what I offered. Our house sold for the listed price after a few months. We had paid taxes on the property for six months at a higher price than the market value.
On another occasion, I helped some older people sell the farm where they had lived all their adult lives. The farm sold for a price that was much higher than what it had been estimated to be worth.
I think that the two examples are pretty common. Many places will "puff up" assessments for businesses and investors and "low ball" assessments for people who have lived in their homes for a long time. There are sometimes formulas for how to do this. One of these ideas is "land use," which means that the property is taxed at its value as a farm, even though it would be a good place for dense residential and commercial development. There are times when there are no rules. It is just done.
Because of these things, it is usually not a good idea to put too much stock in a property's assessed value when trying to figure out its market value. Maybe they are the same. They might be worlds apart.