PS, in my personal life or when writing about other subjects such as on a bb, I am not anal about language and use slang, general or even inappropriate terminology on the regular.
But when we are in our appraisal role, we need to be more precise with our terminology, holding ourselves to a higher standard than RE terminology as it is carelessly or naively used by the general public, RE agents, lenders, and clients, and others..
A client might say , "I want to know the market value of the improvements to the whole property of X acres." Well, there is no market value, as defined to the improvement as a contributory value. They have a value they have. They have a contributory value. That value can be demonstrated in a cost approach or by using an extraction approach.
But there can be no literal sale or transaction of a contributory part of something unless that part is severed off, and then we are back to scrap material or moving a structure off-site.
The problem comes about when appraisers themselves misuse the word "market value .". When the client and the appraiser both misuse the word, the appraisal might pass acceptance with none the wiser. But it still was an incorrect use of what market value means as defined and the appraisal result was construed d as misleading if the application of it were ever scrutinized.