Trans type should be stamped on the trans next to the engine block,
or on a tag fastened/cast to the trans...... on some cars.
Quiko test for Limited slip: Jack it up. Rotate a wheel by hand.
My guess is that both wheels will turn in the same direction, and
a person will not be able to prevent it happening by hand.
If you had a LOCKED Differential, you would already know it,
and wouldn't need to ask the question......
-Bob