The Secret Service now suspects that a bullet fired in this incident may have hit the White House after a bullet round was found in a White House window, though the round had not yet been conclusively linked to the incident.
Technically a "round" is an unfired cartridge, comprising the bullet, the powder, the primer, and the case. I doubt that's what they found in the window; I'm guessing it was the projectile (the "bullet"). I have seen reports saying a round was found on the White House grounds (that's quite a little rhyme!), and this one may be confusing the two.