To start with, dividing an urban area into a city and suburbs, especially when the purpose is to set one against another, is to divide something that's working as a whole. People regularly cross not only municipal boundaries, but urban-suburban-exurban-rural boundaries as a matter of course when conducting daily business. The city and suburbs together form an interdependent economic unit. When my wife's grandfather started his heating and air conditioning business he set up shop in La Grange, a suburb of Chicago, because that was the location from which he could reach the largest part of the area as a whole, from Indiana to Wisconsin, city and suburb alike. A location along the Tri-State Tollway was like a shipping business' location the Chicago Belt Railway. Similarly places we live and work may fit somewhere in a city-suburb binary, but we choose them based on their specific characteristics, convenient access to things we care about, and cost of living. Chicago, La Grange, Naperville, and Skokie are all part of the same whole and all serve each other. Or Seattle, Redmond, Canyon Park, and SeaTac. None could exist as it is today without all the others. The city-suburb distinction sometimes encourages people to set one against the other, especially in funding disputes where one typically accuses the other of being a leech.
And while in some ways the city-suburb binary is an unnecessary and divisive way to look at things, it's also in other ways not precise enough. Perhaps you buy the idea that downtown Kirkland and Canyon Park are both suburban, and that SODO, South Lake Union, and the core of downtown Seattle are all urban. The distinctions within the urban and suburban groups are perhaps greater than the distinctions between them. A lot of people in Seattle live in middle-ground areas developed initially as “streetcar suburbs”, which would further stretch the definitions of whichever group you put them in. And even the history of some of these areas is important. In 20 years people might wonder why all the fast transit service between downtown Seattle (decidedly urban) and the U District (urban enough, and a huge transit destination) skips SLU (which in 20 years will be quite a transit destination). Its history as a warehouse district and its long period of decline will answer those questions well, while an appeal to its “urbanness” won't yield many answers.