What’s the difference between Partial Retrograde Analysis and Retro Strategy? What’s the difference between Partial Retrograde Analysis (PRA) and Retro Strategy (RS) which are different ways of interpreting retrograde analysis chess problems?
The history of some chess positions can be determined with certainty and some cannot. 
PRA looks at each alternative history and finds their different solutions.  These typically revolve around if the right to castle exist, then you have some solution; or if last move allows en-passant then another solution exists.

RS involves 'mutual dependency', for example if a pieces existence on a square can mean either one side can't castle or the other side can't castle; Then the first to castle proves the other couldn't.

There is also the AP (a posteriori) convention, which is controversial as the variations can involve moves motivated more toward proving if certain moves are legal than by real chess motivations.

Tim Krabbé's book Chess Curiosities covers these things.