There are two types of screw-on body jewelry available: internally and externally threaded. Internally threaded, on say a barbell, would have the screw-looking bit on the ball.
The externally threaded jewelry would have the screw-looking piece on the jewelry, like what most screw-on tunnels have.
Sometimes, I’ve noticed people have trouble with irritated piercings, and there can be a lot of factors toward an unhappy piercing (too much movement, not clean enough, too much cleaning, etc). One thing that may play into an irritated piercing is pulling externally threaded jewelry in and out of a piercing- especially a fresh or unhealed piercing. As you can imagine, pulling an externally threaded piece of jewelry through a piercing is kind of like pulling a screw through your hole. Which is all fine and dandy once your piercing is fully healed and not as vulnerable to elements and items.
In the meantime, I’d stick to internally threaded jewelry if you decide to use threaded jewelry on a fresh piercing. This is just my personal preference, but I never realized it until I researched a bit about it. Having the screw-bit inside the jewelry makes insertion much smoother for your piercing. Some people may have issues with externally threaded jewelry, others may not. I just wanted there to be an awareness for the different types out there.