Assessed value is the worth of your home as decided by the city on a yearly basis. This value is then used to determine what you pay in real estate taxes. Every year, the assessed value can go up or down, which can change your monthly mortgage payment.
Appraised value is the worth of your home as decided by a licensed appraiser on a specific day. The appraiser visits the house during the loan process. Why? The appraised value impacts the size of the loan from your lender.