How to fix nail/screw pops in a plasterboard ceiling?

[PG13]

I'm going to be repairing a few cracks in the plasterboard ceiling and noticed a few nail/screw pops. I believe it's plasterboard since the place was built in the 1980s and it's too hard for a pushpin. Do I repair the nail/screw pops like I would a drywall ceiling? Would 1 1/4" drywall screws be ok since I don't know the thickness of the boards? There seems to be contradictory info on the web about what size to use. I'm assuming also 1/2" plasterboards were installed. I think they probably chose the most economical material for these buildings. Thanks

 

[MarineBob]

I'd screw in some drywall screws at an angle to jam against the nails once I tapped them in enough to bury with compound