How a piece opens and closes matters more than it sounds. It decides whether you can change it yourself, and whether it is safe to do so while healing.
Internally threaded
The post is hollow and the decorative end screws into it. The part that passes through your piercing is smooth, with no thread to drag across healing tissue.
Safe for healing. Fiddly the first few times.
Threadless (press-fit)
The end has a slightly bent pin that holds by tension alone. No threads anywhere. Push to seat, pull to remove.
Safe for healing, and the easiest to change once you have the knack. The bend is what creates the grip — if a threadless end keeps falling out, the pin needs a slightly sharper bend, not more force.
Hinged clicker
A ring with a hinged segment that clicks shut. Opens and closes by hand, no tools.
Safe for healing, and the sensible first ring for a daith or a conch precisely because you are not bringing pliers near a fresh piercing.
Seamless ring
A continuous ring that twists open sideways. The cleanest look, because there is no visible join.
Not for healing piercings. Opening and closing one properly takes ring-opening pliers, and doing it by hand distorts the ring and irritates the tissue. Save these for once everything has settled.
Flat backs
Not a thread type, but worth saying: the flat disc that sits behind a stud is what makes it comfortable to sleep on and stops it catching. For anything in cartilage, a flat back is the difference between a piercing that settles and one that stays angry.