Which leaves a muscle hit. Muscle hit blood is crimson color (bright red). The way the deer reacted for you though seems to indicate a stomach/intestine hit.
Yep, those are my two thoughts as well: Reaction says stomach/intestine; color of blood indicates muscle. I've seen muscle-shot deer stop bleeding and go on to live another day. If he's hit in the stomach too, though, I would think he's dead somewhere around there. Check for slight dips, valleys, drainage ditches as well as the thickest briars and brambles it could get into -- especially if around water.