Yea, it's a bit of an arbitrary distinction but I wanted to try to see what types of neighborhoods people are coming from.
In "inner urban core" I'd consider anything within easy walking distance of major employment centers, so not just downtown and Back Bay but also West End, North End, South End, Beacon Hill, Seaport, even possibly Fenway.
"Outer urban core" would be the urban neighborhoods, cities and towns further out - large parts of Southie, Dorchester, Mission Hill, north Brookline, Allston-Brighton, south, north and east Cambridge, Somerville, Charlestown, Eastie, parts of Everett, Chelsea, Malden, etc...
I doubt everyone would agree with that classification, but I thought it's useful to see what 'types" of neighborhoods people are coming from in terms of level of urbanity.