1 British English and American English are different. For example, the equivalent of taking a lift in British English is taking an elevator in American English.
(Ah yes! Also, the boot becomes the trunk, trousers become pants, and biscuits become cookies...)
2 Are they correct?
Is it idiomatic to say a collection counter and an ordering counter where you can order food and collect food?
(No, this usage is not idiomatic, the counter is just named for its function in these cases)