I thought it allowed for you to see the repeater input. But essentially, your explanation satisfies. Repeaters are duplex systems, using two frequencies. The amateurs (Hams) first started using duplex before commercial and public safety people did. They standardized the practice of spacing/offsetting the two frequencies at a set distance and after everyone saw the massive increase in range a properly located repeater afforded, they quickly went to (semi) duplex repeater systems.