We learn a little more here. "Agreement" is the general umbrella that the rest fall under. A treaty is a particular type of agreement. Treaties are dealt with by the President and the Senate. House has no say.
USMCA is not just an agreement, it's a trade agreement. The House does have a say in trade agreements as the Constitution grants Congress the power “To regulate Commerce with foreign Nations, and among the several States, and with the Indian Tribes.