There are quite a few differences between tattoos and piercings, although both penetrate the skin. A piercing is done quickly, while tattoos can take hours. Also, tattoos are more painful than piercings but heal quicker, whereas piercings take a while to heal and can get uncomfortable or even rejected by the body. To prevent any complications, it is important to use longer jewelry.
Otherwise, you can risk having the back of your piercing absorbed into your skin, which can often happen with cartilage piercings. As the piercer of @thecuratedlobe demonstrates in her video of a client having that exact issue.
Piercing complications are always uncomfortable and painful and if not fixed immediately, can lead to skin infections. That's why it is so important to go to a professional piercer who uses the right jewelry - including length and gauge - as both matters.
As you can see in the video, the piercer first cleans the area well with a saline solution applied to the front and back of the piercing. Then she applies a numbing cream to the area and lets it sit for 45 minutes, as it is swollen and irritated. The next step is removing the top of the piercing, using an insertion taper to extract the back of the piercing by pushing it out.
Since the piercing wasn't inflamed and no infection occurred, the piercer just changed the piercing to longer jewelry so it can heal properly, since it was a fresh piercing.
However, in situations like this, it is important to get an absorbed piercing extracted immediately, as it can worsen.