I am royally confused. am i retarded, or am i having a diff problem.

I jacked up my truck, spun one rear wheel, the other spun the other way. I thought this meant NON LSD. My window sticker said i have lsd, my build sheet says i DO NOT.

Went to the mountains today, climbed a slippery hill in 2wd. Both rear tires were spinning. So is this a charachteristic of an open diff in the right situation/condition or do i indeed have the lsd

 

PM me your vin and I will see which diff you have....