Only a couple of centuries ago, the word surgery coexisted happily with the word chirurgery. They came from the same source, but as you can deduce, surgery won out in popular and medical usage. Chirurgery, however, is more accurate, as it is more rooted in the past. Both come from the Latin word chirurgia, from the Ancient Greek word kheirourgia. Up to this point, all the terms still had the same meaning of an invasive medical procedure, but as we go back further, kheirourgia is split into two words: kheir, meaning "hand", and ergon, meaning "work". The combined definition of "working by hand" obviously describes how surgeons go about the job. Kheir is from Proto-Indo-European ghesr, still meaning "hand", and ergon is from Proto-Indo-European wergom, also still meaning "hand". Both likely took a Proto-Hellenic route. In recent years, since surgery has basically driven out all uses chirurgery, it's had room to expand in growth nigh-exponentially in usage, which it has been doing.
Adam Aleksic, a rising sophomore studying linguistics and government at Harvard University, has been described as the internet's sixth most famous etymologist. He also has disturbing interests in politics, vexillology, geography, board games, conlanging, and law.