Moore looks simple and is not. The best-known English sense is topographic: someone who lived by a moor, marsh, or fen (Old English mōr), or who took a habitational name from places called Moore or More. That is why this page's type is place.
DAFN also records Norman nicknames linked to "Moor," Irish Ó Mórdha ("descendant of Mórdha"), Scottish Muir, and Welsh mawr ("big"). US Census Moore therefore mixes streams. Treat the one-sentence lead as the English moor reading, and expect other origins in real family trees.