Market Value is where they compare to simular houses in your area to see what it would really sell for and an Appraisal is where someone Licensed goes to your house and looks at everything(more expensive but worth it).

I associate the term "Market Value Assessment" with Canadian real estate terminology. Here is the United States, one might receive a "Taxable Market Value" from your county tax assessor. It is an arbitrary value and may not based on true market conditions or substantive fact. These subjective values are used to determine how much the property owner will be taxed. Appraisals (URAR / Form 1004) are defensible documents prepared by certified, licensed professional appraisers who are schooled in the skills of real property valuation. Appraisers base their valuations on recent comparable sales and replacement costs. Appraisals are used to determine the value of a real property by individual buyers or sellers as well as institutions who will be lending money for a mortgage. Appraisals will cost $350 and up. A Broker Pricing Opinion (BPO) is a "mini-appraisal" (of sorts) prepared by licensed real estate agents using techniques similar to those of an appraiser, but with less detail. These are used as inexpensive alternatives to appraisals by lenders who are concerned about properties in default or in foreclosure. BPOs cost $75 and up. Realtors may also perform Comparative Market Analysis (CMAs) for homeowners wanting to list their property for sale. A CMA is generally prepared using current sales and listings in the immediate are of the subject property, much the same as an appraisal or BPO, but with even less detail. CMAs are sometimes free of any charge may be credited back upon listing the property with the agent (I price mine the same as my BPOs and offer similar detail). I hope this clarifies matters.

Phil is correct. Market value is usually a price determined by your Realtor who compares recent sales of similar homes and is usually free of charge. Appraised value is a much more thorough comparison of those home value done by a licensed appraiser usually on behalf of your mortgage company and will cost money to have done.