Disinterested party, interested party
This is the whole distinction, and it is not a criticism of agents. An appraiser is a disinterested third party with no financial interest in what the number turns out to be. An agent is an interested party whose compensation depends on the transaction happening and, usually, on the price.
A comparative market analysis is a pricing tool prepared by someone working toward a sale. An appraisal is an independent opinion of value developed under the Uniform Standards of Professional Appraisal Practice, which requires impartiality and requires the appraiser to say so in writing.
I do not prepare CMAs. I prepare pre-listing appraisals, which is a different product from a different position, and I would rather be clear about that than blur it.