No province generates any income of any kind while it is looted. Provinces also do not generate income for their owner when they are controlled or covered by an enemy. There is an exception, though, AIs on normal, hard, and very hard do get income from all owned provinces regardless of the state of the province.
All settlements generate either gold income or production income. In addition, settlements with a center of trade generate trade tariffs, and settlements with a manufactory get manufactory income from it.