Here is the first quote on what happened...
On August 2, 1964, the US destroyer, "Maddox" was fired upon by three North Vietnamese torpedo boats in the Gulf of Tonkin. In retaliation, "Maddox" fired back and hit all three, one of which sank. The "Maddox" then retreated into international waters but the next day it was ordered to return to the Gulf of Tonkin
It is the second day that is in question as to whether or not the Maddox was attacked or not. But the first time it was.