Simply put, it's like comparing opera to country. What the CMA depends on are ill-defined trends. An appraisal relies on comparable sales that can be proven by public record. Location and building prices are also important in an appraisal. The CMA will provide a non-specific figure. An appraisal delivers a defensible and carefully documented opinion of value.
But the biggest difference is who's behind the report. Real estate agents, who may not have a complete understanding of valuation methods or the entire market, write CMA's. The appraisal is produce by a licensed, certified professional who makes a living out of valuing properties. Moreover, the appraiser is an independent voice, with no conditional interest in the property's value, unlike the agent, whose income is tied to the value of the home.