SimonG: GW has since separated the two completely and officially.
Indeed, Chaos is present in both games, with all its gods, and the Chaos Daemon army uses the same models in both games.
But Chaos works differently in the two worlds. You don't have The Warp in Warhammer fantasy, which is where chaos & its daemons live in 40k.
In the old "realms of chaos" books, chaos was described as entering the warhammer fantasy world through two large warp gates, one on each pole. It was the brave Slann that held back the tide of chaos, and managed to shut the warp gates. Slann back then were not like Slann are now, in the old days they were roughly human sized humanoid toads, basically taking the role of the modern day Lizardmen army. Lizardmen back then were larger creatures who served the slann. The same toad-creatures existed in 40k, and had advanced technology. With the release of 4th edition WHFB GW dropped the old Slann army (probably because they did not sell very well), and with the release of 2nd edition 40k the slann were phased out there as well (people don't seem to much care about the old 40k slann, but if you mention Squats whole forums can erupt into pro/anti-squat flame wars). When Lizardmen were introduced as a whole army in Warhammer fantasy, Slann were relegated to a leadership position. They were immensely powerful mages, and a lot larger than a human, and so revered by the lizardmen. In 40k the slann still exists in the fluff, they were even mentioned in the last core rulebook, but they are not a playable army (some people have converted models and use the tau codex to represent slann).
With the slann changed so much, the old fluff was automatically invalidated, it is not left in a state of ambiguity, like a lot of the older Ork fluff. And with it, a lot of the old ties between the games have effectively been cut, so even if GW never had made an official statement about the relation between the two games, the fluff incompatibilities would be enough to make a strong case against it being the same universe.
Still, there are a lot of people who like to theorize about connections between the two. A common theory is that Sigmar was one of the lost primarches.