A college town, in general means, a city small enough that its social/cultural life is heavily influenced, even dominated, by the college(s) located there, especially if it/they are famous. A place can be a college town with only one college, if that college has a dominant place in the culture and functioning of the town.
A big city, even one with lots of colleges/universities, is not going to be a college town because it has many other social and cultural influences.
It is common in the US for universities to have been built in smaller towns where they evolve to be the biggest employer and to alter the character of the town compared to other towns in the region. Typically a college town has more cafes and bookstores catering to students, more live music, more rental accommodation, and generally a more liberal political culture than nearby towns that don't have a college. They also have far more people from "away" living there or passing through. They tend to have cultural elements more typically found in larger cities. Of course the extent of the impact on the town will depend on how self contained the university is.
In such towns almost all the students would arrive from elsewhere and live in dormatories.
The US also has universities in big cities and typically the area around the university will develop into a university district catering to students. Again, this will depend on how self contained the campus is. My feeling however is that since the decline of distinct youth subcultures and the rise of internet shopping, there is less distinctive services in a university district. You are less likely to find used book stores, record shops, or funky vintage clothing, which would have been more common in the 1970s and 1980s.
In the case of Seattle, "the University District" is the name of a specific neighborhood but the last time I visited, it seemed like the "trendy" cafes and shops had set up shop elsewhere.
In Canada universities were typically built in larger cities, and students are more likely to live with their parents and commute, or live off campus wherever they can afford it. As an undergrad I attended a university that was in the suburbs but physically isolated from the community by geography and it generated no university district at all. Students went downtown for fun. There was the regular suburban services closer to campus but nothing that said universy district, just typical supermarkets and diners and gas stations, etc.