A general rule is you can step over brook, jump over a creek, wade across a stream, and swim across a river. But some regions of the state prefer one term over the other, regardless of the size of the waterbody.
The primary purposes of Lake Alice Wildlife Management Area (WMA) are for wildlife management, wildlife habitat management, and wildlife-dependent recreation. The area encompasses 1,468 acres. The principal portions of this management area were acquired in two stages from the William H. Miner Foundation-648 acres in 1953 and 750 acres in 1970. Prior to state ownership, the area was primarily used for agriculture and timber harvesting. In addition, water control structures were built along Tracy Brook to generate hydro-electric power. This mosaic of cropland, woodland, and impounded open water provided an ideal base upon which to establish a wildlife management area. https://www.dec.ny.gov/outdoor/24410.html
Valcour Island is a 968-acre island in Lake Champlain in Clinton County, NY. The island is mostly in the Town of Peru and partly in the Town of Plattsburgh, southeast of the City of Plattsburgh. It is within the boundaries of the Adirondack Park. On October 11, 1776, a naval engagement known as the Battle of Valcour Island between British and United States naval forces under Benedict Arnold was fought in the strait adjacent to the island. Valcour was the site of several farms and summer homes (and one short-lived utopian community, the Dawn Valcour Society) from the nineteenth century until the 1970s, when New York State completed its purchase of the island. The island is now within the Adirondack Park, and is managed by the New York State Department of Environmental Conservation as the “Valcour Island Primitive Area“.