We have plenty of them locally. They're freshwater, empty into the sea, and are affected by tides. Louisiana has its bayous, which are similar. I don't know the origins of these streams of water. They obviously start from somewhere, but I've never hiked the length of one to see, and the maps don't show. It could be underground springs, for all I know. (I took Geology 101, but never took the second semester. Perhaps those classes would have been more enlightening!)
True rivers, at least here in California, are snow melt run-off. There may be other sources, but I'm not aware of them, except for the Truckee River, which starts in Pyramid Lake in Nevada. and ends in Lake Tahoe on the Nevada-California border.