TMetzinger
Final Approach
I think very few pilots carry both, and no certificated pilot is required to carry both. SP's need the logbook but not the medical, and everyone else needs the medical but not the logbook.
The only people required to carry both medical and logbook are non-LSA student pilots, I think...
Rec Pilots need to carry endorsements with them for certain flights. I think the sport pilot regs don't require the actual logbook, but DO require that the SP can show where they've been endorsed for the LSA equivalent of category and class of the airplane they're flying, and any other required endorsements.