Things that are surgical have something to do with an operation performed by a surgeon, or something done with the level of precision a surgeon exercises. So, you could wear surgical scrubs or conduct a surgical strike.
A surgical resident is a doctor who's learning to specialize in performing surgery, and the surgical wing of a hospital is the area where surgery is performed. Because what a surgeon does requires such precision and care, the adjective is also used to describe anything done carefully: "Surgical bombing is supposed to be much more precise, with narrow military targets."
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