Are cable housings different for road/MTB/urban bikes?
Short answer is no.

In terms of normal bulk housing, it used to be that 5mm shift housings were more associated with mountain/utility and 4mm were more associated with road. Now 4mm has become more the norm for everything, although it's kind of a matter of perspective because there are a lot of bikes still running around with 5mm, and you can still buy 5mm. Either works on both, and the common ferrules both have the same OD (there are weirdo ferrules for weirdo frames that need smaller and larger ones, but that's a tangent).

As you've seen, there are various cable kits labeled as mountain or road, and groupset-specific in Shimano's case. There's a couple things going on here. The dimensions of the parts haven't changed - all the mainstream component groups can accept normal housings and ferrules without any adornment. But, the component makers and Shimano in particular seem to have developed certain really specific ideas about what combinations of nosed ferrules and sealing doodads are supposed to go along with which component group, and that's what their group-specific or road versus mountain distinctions are about. Jagwire and other cable set makers have kind of done the same thing. It's all pretty arbitrary in my opinion, but it's a debatable point. The exception is that Shimano is now pushing their slick coated cables very hard for road, and I think that's as it should because their under-the-tape shift routing STIs can have a lot of issues with excess friction being generated at the bar (and that's more or less the reason for the push.)

Also, as was mentioned in the comments, there's some notion that the pre-cut housing lengths in packaged cable sets correspond to road or mountain. Honestly this in my opinion is the biggest reason not to even pay attention to the kits that come with pre-cut housings; the world we're living in now is that bikes have all sorts of different housing/cable routing schemes even within their genres, and you need to just cut it to length and make it right.