There is a "frost line" in the middle of the asteroid belt where you see rocky objects closer and icy objects further. The reason is that closer the Sun has enough energy to sublimate the icy objects into a comet with a tail, where the tail is the icy material being blown off into space. Over billions of years that results in objects with ice-free rocky surfaces inside the frost line, and big, gaseous, volatile-rich outer solar system objects.
So at the time of the formation of the solar system, the whole area was a big gaseous cloud of supernova debris with lots of ice. The ignition of the sun started the frost line, and pushed volatiles out of the inner solar system. However some had already been trapped in the formation of the planets, and rose to the surface as they cooled. That's where Earth's ocean came from, and we know Mars and Venus had oceans too. Presumably also Mercury, although I'm sure that was short-lived.
So yes, it's all from cometary material. But then ALL of the Earth is from cometary material, and the oceans only make up a small amount of the Earth's total mass.
So at the time of the formation of the solar system, the whole area was a big gaseous cloud of supernova debris with lots of ice. The ignition of the sun started the frost line, and pushed volatiles out of the inner solar system. However some had already been trapped in the formation of the planets, and rose to the surface as they cooled. That's where Earth's ocean came from, and we know Mars and Venus had oceans too. Presumably also Mercury, although I'm sure that was short-lived.
So yes, it's all from cometary material. But then ALL of the Earth is from cometary material, and the oceans only make up a small amount of the Earth's total mass.