Treaties among nations involve such things as military agreements, navigation and rites of passage, treatment of foreigners while residing or sojourning abroad, etc.
Commercial or trade agreements are never considered as treaties because they involve revenues in the form of tariffs and only the House can originate revenue bills thereby rendering trade agreements as legislation, not treaties.
This is foundational law in the United States. Trade is never considered in the context of treaty making.
https://www.fas.org/sgp/crs/misc/97-896.pdf
http://conginst.org/2011/12/12/trade-or-treaty-why-does-the-house-approve-free-trade-agreements/
From your link:
“The legislative process for free trade agreements was established in Section 151 of the Trade Act of 1974.”
treaty
[tree-tee]
Spell Syllables
Examples Word Origin
noun, plural treaties.
1.
a formal agreement between two or more states in reference to peace, alliance, commerce, or other international relations.
2.
the formal document embodying such an international agreement.
3.
any agreement or compact.