I hope I have this right because I, too, have been pouring over those two statutes.
776.012 is the right of self-defense.
776.013 is the right to stand your ground.
I think 776.012 and 776.013(3) are repetitive on the instance of use of force in self defense, other than in ones home or car. 776.012 comes first, and points to (incorporates) 776.013 as "other circumstances permitted." 776.013 creates a presumption of reasonable fear (presumption being a burden shifting device) for people in a home or car, then has a subsection (3) that I can't distinguish, substantively, from 776.012.
776.041 also contains a circumstance where the use of force is justified, even if one is the aggressor. This one has a different play against 776.032 immunity, 776.041 not being cited in 776.032.
As to why 776.013(3) exists at all, I have no idea. Legislatures are known to do quirky things. At least 776.012 and 776.013(3) aren't in any sort of conflict with each other.