Medical abortion [1] is commonly known as the abortion pill, and it is a medication regimen that causes cramping and bleeding which subsequently ends a pregnancy. It can be done at home without medical supervision (self-managed abortion) under 11 weeks of pregnancy.
Surgical abortion [2] is a procedure performed by a trained professional, in which the contents of the uterus are removed, thus ending a pregnancy.
Sources
[1] Bpas. The abortion pill. Retrieved from: https://www.bpas.org/abortion-care/abortion-treatments/the-abortion-pill/
[2] Bpas. Surgical abortion. Retrieved from: https://www.bpas.org/abortion-care/abortion-treatments/surgical-abortion/