They started splitting in 1905. Prior to that football was a lot more like rugby. Trouble was, people were getting killed. Every football season there'd be a handful of deaths across the country, and some of the major colleges were actually pushing to ban the sport. It all came to a head in 1905, when 19 people died of on-field injuries, mainly being kicked in the head or rupturing an internal organ.

Teddy Roosevelt -- who was a fan of the game but whose own son had recently been injured while playing for Harvard --- stepped in and helped arrange a meeting of the major college football coaches, which led to a reform of the rules, legalizing the forward pass, and creating penalties for unsportsmanlike conduct and unnecessary roughness. Helmets themselves didn't come in until later, but it's with Roosevelt and the 1905 reforms that establishes the dynamic which has played out several times in the history of the game, where rules have been tweaked to address concerns about too many injuries. The Library of Congress has collected a bunch of original documents and contemporary news reports on the 1905 reforms. Here's a shorter Washington Post summary of the affair.