Just call it Action.  Horror is action, thriller is action, just call it action.

Well, horror HAS action, but it doesn't fit the action model. Most action movies follow a scene pattern of setup>sudden threat>5-15 minutes of non-stop, fast-paced action.

Horror, on the other hand more or less has a known threat before the scene begins or introduces the threat right at the beginning>setup character flaw>character dies (or escapes by the skin of their teeth) after long chase sequence.

Thriller is slightly different in that the threat is known to exist, but generally unknown in origin. It follows a more dramatic model but still along the horror lines of setup>threat made known to audience but not character>long, slow building action sequence>payoff (whatever that may be, whether death or twist).