I have a 67 delta 88 with the 425 HC motor. I did a burnout and both wheels spun. 2 black tracks 8 ft. long. I don't think I have a posi but does anyone know what I do have? from my understanding only one wheel should spin "normally"

 

If its a "posi" or more correctly a limited slip diff jack it up so both rear wheels are off the ground. Now try to quickly spin one side you should feel resistance enough to stop you from spinning that wheel if the clutch packs in good shape. On occasion an open diff will spin both wheels if the suspension is evenly loaded. Some put an air bag in one spring to achieve this.
Is there a rectangular tag attached to one of the diff insp cover bolts? That can be a good sign of a limited slip diff. Remove the cover and look. Clutch packs indicate limited slip. Just spider gears indicate an open diff.

 

I might do that tonight. It could use new lubrication anyways. I'll let you know what I find.