In many countries, the concept of the hospital is also different from what it is in the US.

Where in the US there are clinics, ERs, urgent cares, and specialty practices, elsewhere there's just hospitals and you can go for any kind of treatment big or small.

European here: we have all of those.

Usually for urgent care you go to a hospital if it is not urgent you go to your doctor or walkin clinic.

Nah, there are clinics and specialty practices even in the smallest third world countries.

ER/Urgent care is the same whether it has its own physical building or is a department in a hospital.

None of this has any impact on pricing.