Great question.
I don't think there's any agreed upon definition of suburb or exurb, and the boundary between then is up for discussion. Sometimes, there's a parkland or greenbelt buffer between the two, like in the northern suburbs of NYC - I'd characterize Rockland, Westchester and maybe Putnam county towns as suburbs, and Orange and Dutchess county towns as exurbs, but in other places of the NYC metro where there is no clear demarcation, it becomes harder. For example, where do the exurbs start on Long Island? Probably somewhere in Suffolk County, perhaps where the main lines of the LIRR stop - but it's not clear.
Exurbs do tend to be more recent-growth areas, but not all recent-growth areas are exurbs, particularly in smaller metros.
As someone who has lived in Nassau County my whole life other than college, I'm tempted to say the Sagitkos Parkway is the dividing line on Long Island, but Route 112 is probably more realistic and an argument could be made for as far east as the William Floyd Pkwy.