In Poland municipal, state and federal income taxes are paid as a single entry on the tax form. The government then transfers the money to the appropriate lower level of authorities.
So I wouldn't say that most countries differentiate like in the states.
As an additional data point: provincial income taxes in Canada are collected along with federal income taxes by Revenue Canada and then remitted down to the provinces. The sole exception to this being Quebec.
Definitely a peculiarity of the US system being less cohesive than some other countries - and also dealing with far more people and jurisdictions.
So I wouldn't say that most countries differentiate like in the states.
Maybe it is a Europe - USA difference?