Refugees, though numerous, are not the only war-time migrants; there are also young men either charging into conflict or fleeing from it — all across national boundaries, and thus a form of international migration.
Currently the big story along these lines is that young Russians are fleeing in order to avoid the draft and the heavy casualties. A report from Al Jazeera said that 194,000 Russians had crossed into Finland, (the other) Georgia, and Kazakhstan — just three of the numerous countries sharing a border with Russia.
The reverse flow, of men moving to help Ukraine, is smaller but is useful to that country as a positive symbol. It is said to number in the thousands. The New York Times recently carried a front-page story on how Andrew Milburn, a retired U.S. Marine Colonel, has organized a bunch of foreign fighters there under the (unusual) name of The Mozart Group.
Many Americans went into World War II long before the nation did, flying planes for Chiang Kai-shek or fighting in the Royal Canadian Army and the Royal Canadian Air Force; later, others ducked the Vietnam War, again by moving to Canada.
Recalling stories of large units of the Union Army being recruited from overseas, I recently looked up the flow of international immigrants at the time of our civil war, and found that the Union got seven or eight migrants for every one that joined the Confederacy, an interesting factoid.
Refugees are, of course, much more numerous than these military (or anti-military) migrants, but all of these migration streams are part of major wars.