How do I know if I have a limited slip diff? Did all these trucks come with it?

Most came with standard diff as far as I know... If you look under the hood (on the actual hood) or in the glove box there should be a sticker stating type of driveline installed.

Jack up the rear end with tranny in neutral and turn one tire they should both turn the same way and same speed then its LS. If its jacked up put it in park or in gear if manual and turn one tire, if you can't turn it then you have a limited slip. if it turns and the other turns opposite its an open diff. This works for the clutch style ls diffs. the newer 3ed gen helical gear ls units are not as easy to pick out as they will and do act like an open diff when trying the above technique.