Is my 9 inch rear end limited slip?

I have a ford 9 inch in my 72 4x4 truck. When I jack it up and spin the driver's side wheel, the drive shaft turns but the passenger side wheel does not. If I turn the passenger side wheel, the drive shaft turns but the driver's side wheel does not. If I turn the drive shaft by hand, only the passenger side wheel turns. Since both wheels turn the drive shaft, does this mean I have posi? If so, why don't the wheels turn each other when I turn one?

You have discovered an open differential, my friend.
The side gear for each axle shaft, feeds through the pinion gears and things go round. The other side gear will not get driven by doing that. There are not a set of clutches in operation on yours. Take the tag and clean it, report what it says to your parts counterman at Ford, and he can tell you what parts list it is for.
If there's not an "L" you do not have a locking differential.
If the drive line was turning, therefore the pinion, and in turn, the ring, it would turn whichever axle was giving the least resistance.(The pin thru the "case" transfers rotation to the pinion gears. The case being bolted to the ringgear). Often this is RR. Now, if I were to pull down on the cable for that brake, you could see the other wheel start to spin. Just a matter of fact.