Jim: there are definitions (the one you post is the same as presented in Appraising Residential Properties, 4th ed., AI).
The problem is (and you may agree or disagree with me) the term "market" as typically referenced/referred to in residential mortgage lending isn't adequately defined for what we are really doing.
What we really are doing is analyzing a particular geographic area and then, based on a number of dynamics, identify parts of that area as the competitive market where our subject would compete within and against. Add to the mix the use of "neighborhood" and it can get confusing (even for us appraisers!

).
So, like you, in my residential reports, I include my own definitions (which are not my own, but based on the recognized text) so that the client is not confused:
The Dictionary of Real Estate Appraisal (4th ed.) defines the term "neighborhood" as:
A group of complementary land uses; a congruous grouping of inhabitants, buildings, or business enterprises.
The neighborhood boundaries are: XXXXX
The competitive market is where similar properties compete against one another for the same buyer pool. "Competitive Market" is defined as:
The geographic or locational delineation of the market for a specific category of real estate, i.e., the area in which alternative, similar properties effectively compete with the subject property in the minds of probable, potential purchasers and users.
The competitive market boundaries are: XXXXX
See addendum exhibit "Subject Competitive Market/Transaction Summary Table" for a map of the competitive market area and a summary of the sales transactions per MLS.
My neighborhood may be the same as my competitive market, but I've yet to conclude my neighborhood is bigger than my competitive market.