I used to cut a little bit as a teenager, but getting any kind of blood draws or injections hurts like hell and usually bruises my arms up a lot afterwards. I still have bruises on my arms from a blood draw that happened two weeks ago.
Despite having a lot of blood tests, IVs, and even surgery, I still panic before any needle goes in and I will always despise it. My veins are not great so there have been ocassions where I will get stabbed or fished with the needle multiple times, which is excruciatingly painful.
With self harm, I think the pain is more controlled and self-serving, and is usually done as a means of catharsis. When you have control over the situation and are inflicting the pain onto yourself, it is a different context than being in a medical environment where you don't really have control over the skill of the nurse or technician. You can't control the force of the needle, the depth, the angle, or anything like that.
Ultimately, others cannot predict our pain tolerance or perceive sensory input the same way we would, so it's a lot harder for medical staff to control the level of pain they inflict on you. If you're dealing the damage yourself, you can control what happens throughout the entire thing, and can stop when it becomes too much. In medical contexts, you don't have that liberty and the level of pain you will experience is contigent on the skill of the person handling you.
That's why it's different, imo.
