A normal diff will send basically, jst send more power the the wheel with more traction, its not locked, so both wheels dont get equall power, if you jack a FWD car without a diff up, anbd dtart it in gear, it will just spin the jacked up wheel and stay still.

A LSD or ATB (limited slip diff or anti torque biasing diff) will send closer to equall power to both wheels, so instead of just spinning one wheel, you will spin both up, more traction and better (once used to it in FWD) handling.
thats about all my knowledge on them, i'm sure someone else will give you more info!