Where are you referring to where there are only two city types? I live in the Netherlands, neither of the two existing models you describe sound familiar in any countries around here, although our cities were certainly designed in a low tech past.
Rotterdam, The Hague, and Utrecht (ok, not Holland...) had mass amounts of people from surrounding villages (essentially suburbs) with longer commutes to work in the city (model 1). I knew several people who worked in these cities and had a daily commute of 40 to 60 minutes one way for university or work.
A lot of Amsterdam can be seen as a densely populated area facilitating moving people from residential areas to commercial for work (essentially model 2). It absolutely has a rush hour of people commuting from both the surrounding areas and different neighborhoods; this is seen in both car traffic, trams, taxis, and trains. Many other large cities in neighboring countries (e.g. Brussels) would also fit this description.
These might not be a 2-hour commutes, but it's far from living, working, and shopping in your neighborhood.
[0] https://en.wikipedia.org/wiki/Ruhr an area in Germany close to the Dutch border