An open diff will have the tires spin opposite each other when jacked up. You can spin one tire if it is jacked up while the other is on the ground if trans is in Neutral.
LSD tires will spin in same direction when jacked up. Will not allow you to spin the wheel with only one up in the air.
This assumes the driveshaft is installed too. If the d/s is out, or in Neutral then a LSD will a tire to spin. The whole point of the LSD is to keep both tires engaged for better traction.