A commerce agreement is not the same as a trade Agreement.
A trade agreement specifies exactly what is authorized to be traded whereas a commerce agreement is general in allowing the traffic of commercial vessels or cargo to pass unfettered or unmolested through certain regions of control.
Assuming what you say is true, then nearly every trade agreement including Nafta and TPP would have to be considered a treaty because they cover a lot more issues than authorization for goods to be traded. They include such things as immigration, access to markets, access to ports and highways and rivers. I'm sure TPP contains all kinds of crap about global warming and limitations on the rights of Americans to drill for oil, mine coal, drive SUV's......
So how can Nafta and TPP not be subject to the treaty clause?