I listened to the Battleship Pretension podcast episode just this week to prepare for this inevitable discussion. It's a pretty good ep, though a little ragged.
BUT, the best point the make in the difference between suspense and horror is the release of tension. Horror movies build tension up, but there is never any real payoff or release...you're just scared/uncomfortable (or at least that's the goal).
Suspense films generally build up tension and there is more of a payoff when that tension is released.
IMO, one major factor that would sort of limit what can be considered horror is any whodunit element. If there is a mystery that is being actively investigated by someone other than those immediately involved in the "incident", then it's a suspense/thriller movie. In these movies, the viewer is generally more concerned, or least partially concerned, with following the plot and the mystery. MOST horror films don't have the same kind of "procedural" feel. There are some that have similar auras about them, like Rosemary's Baby as an example, when we start to unravel what the hell is actually happening. But it's not done in the same style as something like Silence Of The Lambs.
Of course, no rule or guide will really hold up perfectly, but the debate is definitely interesting.
I thought they said that horror had a payoff for the suspension?