Adj means any abbreviation for adjective in most cases. It can also have other meanings, i.e. be used for other types of abbreviations.
Adj usually means an adjective in the form of an abbreviation. It also means terms like adjutant or adjourned. It could also be an abbreviation for adjustment. It could also mean adjoining or adjacent in the real estate spectrum.
Adjacent has direct relevance in real estate. It means any property which is next to another one. The same holds true for adjoining in case the Adj abbreviation stands for the same. At the same time, it could mean adjoining properties or houses, apartments, or other units, which are directly in contact with other units, houses, apartments, and structures, or share common walls.