The US is party to at least 5,000 ‘agreements between nations’ that are not treaties.
Well, yes. But a line has to be drawn between a low-power agreement (like: I won't tax your wheat if you don't tax my steel) and a high-power agreement like the TPP. I would argue that that line should be drawn as conservatively as possible.
If such an agreement has sweeping powers, or the potential for such powers, it's a treaty.
Sorry FRiend, but they are all treaties.
trea·ty
A formally concluded and ratified agreement between countries.