In Ireland, most buses are run by CIE, a state company. In Dublin, for the last couple of decades, some routes have been run by GoAhead, a private company (Dublin Bus (part of CIE) and GoAhead tender for the routes). It's been a fascinating experiment in privatisation; the buses all use TFI livery, so the only way to tell whether your route is run by Dublin Bus or GoAhead, besides looking it up, is that if it's Dublin Bus, it'll just be late; if it's GoAhead it won't show up at all. For all that people complain about public sector inefficiency, private companies turn out to be very, very bad at competing with the public sector.

- a company run the busses

- its partially of fully owned by the city/state, i.e. NOT private investors, not private liquidity, no one expects any payouts

- its commonly a special form of "company", e.g. "Anstalt des öffentlichen Rechts" in this case which you can roughly read as "installment/company based on public-law"

Practical that is "mostly" the same as state run when looking at it from a distance. But with some differences. Like it's still a company, has it's own company structure, it's own bookkeeping, it's own employees etc. This leads to a much more clean separation when it comes to budged managing, and where possible removes/reduces direct political influence into daily operations (just direct one, indirectly through ownership etc. there is very much still influence, but this makes it somewhat less suspect to damage from changing political parties non stop changing directions).

Through things can get far more complicated then just one company, in one legal form.