I shared this mental model until I read "The Almighty Dollar" by Brendan Greeley. Highly recommend! It shows how we moved through a few different monetary regimes in the 19th century, including regional variations and private banknotes. Spanish silver dollars were also widely circulated until 1857. The greenback wasn't introduced until the Civil War. Reliable convertibility of federal notes to gold was the exception, not the rule, available c. 1879-1933.
https://www.penguinrandomhouse.com/books/634502/the-almighty...