Ask the New York Appraiser

Property assessments are not an appraisal. The property assessment is not as thorough as an appraisal and, actually, part of the appraisal business is often involved with fighting assessments that are too high. While the assessor is trying to be fair, he does not usually have the resources available to him to evaluate each property as thoroughly as an appraiser could. 

A CMA (certified market analysis) or BPO (brokers price opinion) are not an appraisal. While brokers are usually knowledgeable about the market, they are brokers, not licensed appraisers, and some (even if only a few) may have their own interests when performing a CMA or BPO.  It's a good idea, actually, to have an appraisal done to get an unbiased estimate of value.

A home inspection is not an appraisal.  While appraisers note obvious visual structural problems, real estate appraisers are not licensed home inspectors or engineers. The appraiser represents the lender. If you are purchasing and have questions about a property's structural integrity, you want to also hire a qualified home inspector to answer those questions.