Currently, coastal nations can claim an “exclusive economic zone” up to 200 nautical miles offshore, where they have specific rights and jurisdiction for certain limited purposes, including managing fisheries and ecosystems, producing energy, and conducting scientific research. On the other hand, international waters are governed by the United Nations Convention on the Law of the Sea, and they are not under the jurisdiction of any nation. All states have to right to lay cables/pipelines, to fish, to fly over the water, etc..
All vessels (including military, transportation, and other ships) enjoy the right of innocent passage in all ocean waters. This means that vessels may expeditiously transit territorial waters as long as they do not engage in certain specified activities deemed to disrupt the peace, good order or security of the coastal state.
On this photo, EEZs are shown in light blue, international waters are shown in dark blue.
https://upload.wikimedia.org/wikipedia/commons/c/c7/Exclusive_Economic_Zones.svg