The appraisal is an estimate of value provided by a certified Appraiser, usually on behalf of a lender, but also sometimes for a property owner. It is based on sold properties, that are similar within a certain time frame, and sometimes they also do a replacement cost estimate.
The second part to question can be answered a couple of ways. Property value is simply what a buyer is willing to pay to a willing seller. Again, usually the value is determined by comparing similar properties that have recently sold.
Or you can check the tax records for the tax appraiser's determination of property value. You may already be aware, however, that the tax appraiser's valuations are far different than what a lender's appraiser may determine to be the value of a property.
I hope this helps. If you would like to continue this conversation, please send me an email privately.