The definition of 'suburb' has been changing over time. I can't speak to Detroit but for instance with Boston the original 'suburbs' would now be described as "the city of Boston, not its suburbs". Likewise the town I grew up in as a kid (mumble) years ago, I would have been laughed at for calling it a 'suburb' of Boston as it was too far out of the city. Now Wikipedia calls it a suburb of Boston.