Please provide more information, like years this occurred. Yes the areas we know as Syria and Iraq were part of the same empires at one time. Be they the Persian, Roman, Ottoman, etc. But the people of the two countries are not the same people. Just in the same way Czechs, Slovaks, Croats, and Austrians, to name a few, all resided within the Austro-Hungarian Empire at one time. They were not all same people because of this.
I mean the maps I used as a kid had the area labeled as “Syria-Iraq”. I can’t get any plainer than that.