For counter service, think " go up to a counter, order food, and carry it to a table myself". No waiters or waitresses. Counter service is just another name for fast-food restaurant (but without the drive-thru. )
At Mexico, the counter service place (Cantina de San Angel)is outside of the Mexico Pavillion, across the main walkway, adjacent to the World Showcase Lagoon. You've probably seen people sitting there in the late evening waiting for Illuminations to begin as the table area has a great view.
The sit-down, "by the river" restaurant ( San Angel Inn) is inside the Mexico Pavillion.
The Quick & Casual lunch or dinner vouchers save you a lot at Beaches & Cream and Pepper Market (at Coronado Springs). We used vouchers at both places and the meals we got would have cost over $50. With the vouchers it was $21 (for 2 adults). There are a few places like this that are not "counter service". At most other places the vouchers are good for it is true counter service and you only save a couple dollars.
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