It counts steps every time your arm moves in a way that is similar to the movement experienced when stepping. Brushing teeth is a classic example (if you wear it on the hand you brush with).
I can't comment on the left right observation.
Mike | London, UK
Blaze, Surge, Charge 2, Charge, Flex 2 - iPad Air 2, Nokia Lumia 925 (Deceased), iPhone 6
Take a look at the Fitbit help site for further assistance and information.