In my books, there are three main forms of currency. First, we have copper coins. They are worth very little (for example, a good Serice pancake costs around 100-150 copper coins). Copper coins are typically carried with a string through the open hole in the middle, and a string of coins is usually close to 1,000 coins.
The second unit of currency is the silver cat, which is a small ingot of silver, roughly shaped like a sleeping cat with its tail curled around (forming an oval shape). The silver cat in Serica is roughly equal to a string of 1,000 copper coins. A person can barely get by on an income of one silver cat per month.
The third unit of currency is the Salt Note. A salt note is worth a certain amount of salt from the government’s salt supply (in Serica, the government has a monopoly on salt production). Typically, salt notes are worth half a wagon load of salt, sometimes more. This usually translates into a value of five to ten silver cats, and it varies based on the current price of salt. Salt notes have been used in the past and, in the past, they have been rendered completely worthless by the overprinting of salt notes by unwise government officials.
What relation does this have to China during the Song-Yuan-Ming era? For copper coins, this is pretty accurate. There is a funny story from Vietnamese history where the government sold tons of rice to Chinese merchants (a normal thing to do) but they only accepted copper coins in payment and the Vietnamese government then melted the copper coins down to help them make bronze cannons. Copper coins were very, very cheap. Really too cheap but the Imperial government made the coins in vast quantities, year after year, century after century. You can easily buy 1,000 year-old copper coins today because so many were produced in every decade.
As for silver cats? This is sort-of accurate but not exactly. Silver was the main transaction currency for large purchases in China but silver coins were rare. (And, for reasons that are still mysterious, gold coins are virtually never to be found!) In the Ming Dynasty, silver coins were never minted and so everyone had to use small ingots or pieces of silver. These were called taels in the north, and sycee in the south. A larger unit of silver (16 tales or more than a pound) was called a catty. I took the word catty, and voila! The silver cat was born.
And the salt notes? Are these real? Yes, these also are based on the history of China. The Song first used paper money to create a contract such that the holder of an official salt note could obtain a fixed quantity of salt from the Imperial storehouse. In theory, the only way you could get a salt note in the first place was to deliver supplies to one of the northern forts. The fort quartermaster would then give a merchant some salt notes in exchange for the supplies, and then the notes could be redeemed back at the capital. By adjusting the value of the note compared to the value of the supplies delivered, the government could get food and materials delivered to the northern forts “for free”. By accident, the Song created the first bank notes which were widely used throughout the Song lands.
Unfortunately, the system of paper money was misused at the end of the Song Dynasty and thoroughly misused by the Mongols (Yuan Dynasty). All it takes is to print more salt notes than you actually have salt available and the currency begins to drop in value. The loss of confidence in a government’s salt notes is not usually fixable and soon they are worthless pieces of paper. The Ming “solved” this problem by not issuing salt notes at all (at least not after 1380~). Under the Ming, all big transactions had to be done via ingots of silver or gold. And so the silver/gold had to be first assayed (to make sure the silver wasn’t mixed with some worthless metal) and then cast into small one-ounce molds, because who wants to carry around a single large brick of silver? No one does.
I recommend the Shanghai Museum, it had a great section on currency when I was there in 2015.