LSD limits the difference in rotational speed of two sides of a differential, up to and including total lock up (both shafts rotate at the same speed).
Normally a differential allows unlimited difference in rotational speeds of both sides, up to and including 100% of torque to one wheel and 0% to the other. Unfortunately, with an open differential (no LSD) the most torque goes to the wheel with the least resistance. That's how one wheel can be on ice and spin like crazy and the other just sits there like a lump.
Traction control is something totally different.
Traction control limits the amount of wheel spin. A variety of methods can be used from cutting fuel to cutting spark, or both. Often times a TC system will cut out individual cylinders to limit the power that gets transmitted to the wheels.