I prefer to categorize them as "absolute past", "absolute present", and "absolute elsewhere". This is because for any event in one of your light cones (past or future), there'll be a reference frame that places it at your location (i.e. the same spatial coordinates, just at a different time). But for events outside your light cones, no reference frame will have it at the same location; it's absolutely elsewhere.

BTW, if you also want to talk about the present, you can only talk about it at a particular location. If you want, you can define 3 "thin" boundary regions: the surface of the future light cone (boundary between absolute future & absolute elsewhere), the surface of the past light cone (similar), and the "here & now" (the single point in spacetime where all 3 regions meet).