An assessment is determined by an assessor, employed by a government for the purpose of determining property taxes in a given year. Sometimes assessments are determined by applying algorithms.

An appraisal prepared by an appraiser is a formal document that considers past sales of comparable real property with adjustments and is only valid for the date of the appraisal. Appraisals are used in lending, expropriation, taxation, divorce, legal and other formal proceedings.

A comparative market analysis (CMA) prepared by a real estate licensee considers the entire real estate market (comparable past sales and active listings and expired listings) in order to determine a likely sale price in the near future.

Great answer from Larry.

Assessment - Each taxing authority establishes their own criteria for this value. Those areas with independent taxing authorities makes projecting of future taxes a very imprecise activity. (I do track this value in the CIS Score)

CMA - a resource provided by a REALTOR using comparable sales and relies heavily in the skill and experience of the REALTOR. 

Appraisal - a resource used primarily by lenders to ensure the property valuation falls within predetermined standards of the lender. Having an appraisal completed before placing property on the market identifies the obstacles that must be overcome and from whom you should accept a purchase offer. Many times the buyer is willing and able to pay more than the appraised value. Again, this does allow the appraiser to influence the outcome (they know what the bank wants and want to avoid being listed) and it varies based on the instruction imposed by the bank on the appraiser.

BPO - an evaluation done on the cheap. Usually requested by a lender to establish a list price and again for the last round of negotiations. There was one guy advertising to do a BPO for $8. 

CIS Score - an objective evaluation process whose baseline is established by community sales. After normalization, the value of the home is calculated thorough assessing the tangible assets of the home. These assets are valued based on binary responses to very narrow questions. The answer are either yes or no. There are no subjective components

A recent sale had the following outcome:

List Price $275,000

Sold Price $260,000

Zillow - $231,000  (11%)

Tax - $212,110     (18%)

Appr - $250,000   (4%)

CIS Score - $267,454  (3%)

For homes under $800,000 the accuracy of the CIS Score has been averaging within 4% of sold price.

An appraisal is the figure that has the clout with the lender and the buyer so that make it more valuable. An agent that really knows the market and shows lots of homes will have a more accurate CMA than the general appraiser can give. I have substantiated that with many appraisers that call me to validate their appraisals. They realize I know the market better than they do.

Different forms, and different methodologys.

Learning.

Assessment is for tax purposes and different states have different rules, the other two should be similar.

Never heard of #1

In my area, an appraisal must be done by a licensed appraiser. I can do a CMA or BPO, but not an appraisal. 

The city's assessment only takes finished square footage into account, and determines a value per finished square foot in order to generate a tax value. It does not make any adjustments considering the quality of the interior.

The CMA is created by an agent, and takes both the finished square footage and the quality of the interior finishes to determine a value relative to other sold houses in the neighborhood.

When I became an agent over ten years ago, the head of my office told me that there were two different kinds of appraisals - one that was a more objective evaluation of a house to provide its true value, and the other in order to qualify for a refinance. Of course, this second kind was much more lenient, more likely ot be a drive-by, and more likely to overvalue the house in order to justify the refinancing. This was back in the day the the banks and lending institutions had preferred appraisers that they could call on to enusre the "correct" appraised value, ie, "If the appraised value does not match what we need, you don't get paid."

After the Dodd-Frank Financial Reform BIll of 2008, these lending institutions have a more "arms-length" relationship with the appraisers. Hell, sometimes the appraisers even come from different counties to make sure that the ppraised values objectively reflect a true market value. This has negatively affected these appraisals, I feel.

Some of the BPOs that some companies ask for now are so detailed that I believe that the sometimes-bogus companies that order them actually use them in the place of an appraisal...

Assessment - the value of home in town's records

CMA - perceived market value of a home by a real estate professional

Appraisal - Valuation of a property by a professional appraiser.

Evelyn, I would explain the difference with who is preparing it.  Assessments are usually done by taxing authorities, comparative analyses by Real estate agents, and appraisals by appraisers.

An assessment using set standards of values for everything included in the property like square feet of concrete in a driveway, etc. It doesn't reflect the true condition inside because they almost never get inside so it is an exterior assessment based on their measurements and county permit data.

A CMA uses sold comparables but again the agent doesn't know what the other houses look like unless they take the time to look at MLS pictures or they have shown the property.

A BPO is generally a drive by exterior expecting the interior to be in the same or worse condition as the outside. When I was doing these I always made large adjustment deductions for condition. Even then they often sold well under these BPO prices because of the interior surprises.

The CMA is the closest to true market value for me.