I think in general they are synonymous. Watershed, catchment, basin... these terms all mean the same thing, really (to me). They are confusing because these words or parts of them are sometimes used for other drainage related things: catchbasin, detention basin, watershed (as the ridge line or watershed divide), etc. ... I'm sure I'm missing others and some people may disagree with my definition of these terms since their "culture" used them differently than mine.
In Arc Hydro, "Catchment" is the default name used for the the "watershed" polygons that correspond to the stream link (strlnk) grid. These do not overlap each other.
In Arc Hydro, "AdjointCatchment" is the default name used for the the "watershed" polygons that correspond to the stream link (strlnk) grid. These overlap each other. They are used as part of the geo-network to make delineation of the watersheds very fast, the whole reason behind the DrainagePoint, DrainageLine, AdjointCatchments layers and HydroIDs, NextDownIDs, DrainageIDs in the first place.
In Arc Hydro, "Watershed" is the default name used for the the "watershed" polygons that correspond to the BatchPoint points. These overlap each other. That is, the Watershed polygons include all areas that drain to the point per the flow direction grid.
In Arc Hydro "Subwatershed" is the default name used for the the "watershed" polygons that correspond to the BatchPoint points. These do not overlap each other. That is, the Subwatershed polygons include only the areas that drain to the BatchPoint per the flow direction grid below any upstream batch points.
If you don't like the default names, you can always change them. I used to until I got tired of doing that. Eventually, I just embraced them.
Of course, this is just my understanding. You may find better information elsewhere.