Appraised value usually puts the most weight on past history of real estate sales. Market value can differ as real estate market dynamics can quickly change course making past sold values irrelevant.
In a rising market, I will put a lot of weight on recent pending sales (properties in escrow waiting to close) in addition to the supply and demand ratio of available homes for sale compared to the volume of recent pending sales activity. In a declining market, yesterdayâ€™s sold property values are usually higher than what a property is worth today. I usually put a lot of weight on the value of competing homes for sale in addition to the supply and demand ratio and lengthening marketing time to sell a property.
Appraised value is a "likely sale price" usually conservatively arrived at if done by an independent appraiser. If the appraisal is being done for sale or refi then the number is the target but it is the appraisers responsibility to protect the lender.
Market value is the price "an able buyer will pay" for the property and is subject to current market conditions.