I think the divide is between those who are frum first and part of their general society second, versus those who try to bend frumkeit to match secular social and moral norms so that they can blend in while keeping the bare essentials. The first are guided by Torah and daas Torah – the second by the society around them and dass baal-habayis.
The first group are defined as charedi by some. Still, you’ll find plenty of the former in MO, especially in YU. The latter are more socially frum than anything and you’ll find them at the margins of the yeshiva and chassidishe velt. Nevertheless, they are far more prevalent in the MO world.
However, those who profess the second as an ideology are found only in MO (and RZ in EY, where you still have a hard core for whom tzioinis is more important than Torah to the point they believe that Knesset decisions have the force of Torah).