Contrary to popular belief, Cape Horn is not the southernmost point of mainland South America.
Cape Horn is farther south in latitude because the Tierra del Fuego islands extend below the mainland. Historically, rounding “the Horn” was the maritime milestone, so it captured the imagination.
If you count all Chilean territory, Águila Islet (56°32′ S) in the Diego Ramírez Islands is the southernmost land. The South Pole lies on the Antarctic continent, which Chile claims a sector of.
Mainland: Cape Froward. Island (classic maritime): Cape Horn. Absolute Chilean territory: Águila Islet.