Intended User defines more than just the client.

The value of a property can vary depending on its intended use which would be conveyed in the appraisal request through the Intended User.  For instance, the value of a single family home can vary between an investor purchasing for financial return and a family seeking a home for themselves.  The first would be based primarily on the Income Approach, which along with the Market and Cost Approaches, combine to be the three approaches to value required by USPAP to be considered for any appraisal report.

The example you provided of a refinance appraisal being used by a borrower as an indication of listing price is not unusual and has its roots in the practice of recent years where unethical mortgage lenders would coerce appraisers to meet specified values to allow loans to go through.  Please don't interpret this as being either right or legal.  We are now paying the price in the financial markets for these abuses.  Good appraisers refused to meet these values at a loss of work since those lender would no longer use them for appraisal work.  According to USPAP, an appraiser must be competent to appraise a property, this includes familiarity with the local market.  Unfortunately, since appraisals licenses are issued on a statewide basis, hungry appraisers from markets outside the subject area, accepted assignments and met values (sometimes unknowingly but more often with awareness) for these loans.  This is a very common occurance in Northern Michigan where downstate companies attempt to service the entire state with no true market knowledge of the local areas.  The result is that they use comparable sales from more highly valued neighborhoods, thus inflating the value.  The result has been the upside down home-owners who now owe more than their home is worth.  For whatever reason (credit card debt, new care, home repair, illness, etc.), they needed additional money beyond the true value of the home.  While the common outcry in the media is subprime borrowers with little equity, often appraisal values were inflated by the afore-described manner to make the loan appear to be a highly secured loan of 60-80% LTV.  Loan officers shopped around to appraisal companies until they found one who would provide the value needed.  Nothing in this proces was either ethical or legal.  It is a point of frustration for the large percentage of good appraisers that this was done.  Lenders have gone to extensive means to sidestep the required appraisal documentation for the loan security.

By definition, an appraisal is an estimate of value, not a science.  Valuation by several different appraisers should result in a value range which is somewhat consistant, but a range nonetheless.Valuation for insurance could be for replacement or reconstruction costs which vary greatly and also do not include the land value since the land remains after catastrophe.  For many years, real estate agents provided valuation for estates but this has recently been corrected by an IRS requirement for valuations to be performed by a defined "Qualified Appraiser".  With BPO's performed by brokers not extensively trained in appraisal practices and procedures, these values placed among professionally appraised values can expand the range.  Since assessors analyze market sales to assess properties, often they lack the overall understanding of market trends to properly interpret the results they find.

While more extensive than you may have desired, I hope this sheds some light as to value variances.