Terms, Glorious Terms!
Loan-to-Value Ratio (LTV):
When you divide the value of the property, set by bank appraisal, by the amount of the loan, you get the LTV or Loan-to-Value ratio.
Traditionally, if your LTV is 80% or lower, you get more favorable mortgage interest rates.
If your LTV is higher than 80% you may be forced to carry Private Mortgage Insurance (PMI) which is a monthly insurance payment necessary to insure that in a case of default the mortgage will be covered.
PMI, in almost everyones eyes is a bad use of money. You pay a premium monthly and get little or nothing in return, the mortgage company benefits.
Property Value: Appraisal vs. Assessments
When folks talk about their property they often look at it's value in the broadest sense. What they feel it will bring in the current market compared to other properties on the market, or currently sold. Though this is the basis of a bank appraisal, it's not the same.
An appraisal is an analysis of a property done by a licensed real estate appraiser who is hired by a lending institution to value the property that is being considered for purchase to see if that property is worth the mortgage amount.
Value of a property as seen by the local municipality for tax purposes. In Massachusetts this is an interesting phenomena, all in itself worthy of future treatment on it's own, but suffice to say, this is the assumed fair market value of a property as determined by the local Assessor.