I disagree that queue is exclusive to British dialects. Some American dialects also use the word queue, especially to distinguish a line from a queue.
There isn't a hard distinction between line and queue, it is more of a soft distinction. If you use line instead of queue everyone knows what you mean, but a line tends to be less formal.
Most cafeteria style eateries have queues. Even if nobody is waiting ahead of your party, you still have to walk through a queue. A line usually only exists while multiple people are waiting.