Appraisers provide a service which is one of the hallmarks of a profession. However we produce a product, which is a component of one definition of a industry, the production of a product. So, real estate appraisers provide both a service as well as a product.
My opinion and the opinion of others is that real estate appraisal is a profession. Here's why, part of the definition of a profession requires the practitioner to master the knowledge of some department of learning or science. As a real estate appraiser there is a body of knowledge which I must learn, then master, to provide my service, competently.