Sorry to hear of your loss. Big hug.
And totally agree that the names are dreadful! They need to remain the three possible ways to manage a miscarriage.
I had a natural miscarriage. I was due to have a medical management one the next day but my body took over.
Mine was a missed miscarriage as the baby was only about 6wks according to the scan and we thought we were close to 10 weeks.
I found a natural miscarriage very painful because I wasn't on strong pain killers and I did have to be rushed to hospital and was kept in overnight.
Tops of my legs ached and my stomach felt like it was being torn apart. I also started throwing up. I have heavy periods and this was much more painful than cramps because I just couldn't get comfortable.
I passed two large bits and each time it was painful but when I had the right painkillers it was manageable and only lasted a few hours. I also bled like a heavy period.
If you opt to have a natural miscarriage ask the doctor to prescribe you with Naproxen or something as strong. It can make you bleed more but it's strong stuff. They give it to women after a C-section.
I'm scared of operations so a natural miscarriage was the best option for me.
Go for whatever suits you best.
Make sure you a) have people around to look after you (my husband lay alongside me when I was in pain and it really comforted me) and b) tell people to send you flowers after the hospital bit - it helped me!
Thinking of you.