Does the location of the double bond in chlorins yield a distinct biological function?
I only found a hint that this might be the case in this publication by Singh et al., stating


  Porphyrins, chlorins, bacteriochlorins, and isobacteriochlorins each have unique photophysical properties that are exploited by nature and can be used for diverse applications (1, 2).


I don't have access to "The Porphyrin Handbook" (The first citation in the quote above), but I suspect it would be your best guess in finding more information.