The war that John Steinbeck discusses in "Symptoms" is the Civil War. The Civil War was fought between the North and the South of the United States from 1861 to 1865.
The war that Tim O'Brien writes about, on the other hand, is the Vietnam War. We know this because he describes being at My Khe. The Vietnam War was a war between North Vietnam and South Vietnam (with American involvement) between 1955-1975.
