I think the strictest definition of U.S. history is the history of the state.
But history is a bit fluid in that it's not beholden to specific national borders. And we might study the history of the land the U.S. occupies and colloquially call it U.S. history even though most of it happened before there was a U.S. and may not always follow the current borders.
And I think there is a clear distinction that can reasonably be made if someone is referring to the history of the state or the history of the land and be conscious that they're not always mutually exclusive.
But history is a bit fluid in that it's not beholden to specific national borders. And we might study the history of the land the U.S. occupies and colloquially call it U.S. history even though most of it happened before there was a U.S. and may not always follow the current borders.
And I think there is a clear distinction that can reasonably be made if someone is referring to the history of the state or the history of the land and be conscious that they're not always mutually exclusive.