The term "one signature paper" applied to a specific period of U.S. Notes, and it's a bit of a misnomer. Here's the breakdown of why:

What U.S. Notes Were ("Greenbacks")

Civil War Financing: Issued first in 1862, these were a way to pay Union expenses when traditional revenue wasn't enough.
Not Backed by Gold: Unlike some prior currency, they were "fiat money", their value based on faith in the U.S. government's solvency. This was controversial at the time.
Legal Tender Status: Despite debate, they were made legal to settle debts. This is key, as otherwise their value would rely on who voluntarily accepted them.

Where the Signature Confusion Arises:

Early Designs: Initially, the only signatures WERE the Treasury Register and Treasurer. This visually separated them from earlier notes with bank officials' signatures as well.
Multiple Series: Over time, U.S. Notes had design changes, including different combinations of signatures.
The Red Seal: The distinctive red Treasury Seal was more consistent than which specific officials signed. This may contribute to the misconception of "all being the same" in terms of backing.

Why "One Signature" Isn't Quite Accurate:

While the term is colloquially used, it simplifies a complex history. Even in the early years, some smaller denomination U.S. Notes had additional signatures for anti-counterfeiting purposes.

A More Accurate Framing:

It's better to think of "one signature" era notes as highlighting the shift to a centralized currency model where:

Federal Government is SOLE Issuer: No more patchwork of thousands of different bank notes.
Value Tied to Trust: The signature(s) represented a promise the U.S. stood behind its money, even when not directly linked to a stock of gold.