It is a bit more complicated than that, mostly because the US isn’t a signatory to unclos, while China is. However, China does not recognize the agreed upon terms of unclos, while America for the most part does…
but news media needs to quit exploiting the fact that readers don’t know the difference between different types of waters to manufacture “more-interesting” stories.
The problem is that there is conflicting information on how the states in question interprets what they and others can do in EEZs, and how the EEZs are constituted in the first place.
In reality an international body of laws like unclos is only enforceable if the international court is willing to confront its members with hard power. Withholding that, it’s just a dog and pony show that has the possibility of validating an international conflict if someone oversteps their mark.