We should strive for simplicity in our monetary system, especially in terminology.
Using the U.S. as an example, for paper money, bills come in 1, 2, 5, 10, 20, 100, and 1000. But there’s only one name for all of them: “dollar.” And yet “dollar” really describes “one” accurately. If I give someone a $100 bill, that’s how I say it: “one hundred dollars.” Unless I specify which bills I gave, you have no idea what configuration of bills I used. Now imagine that that $100 bill has a name, dellium. Then I could say, “one dellium.” The problem here is that the audience has no idea that a dellium is one hundred of something else. Explaining it is a poor use of exposition, it won’t be remembered, and it doesn’t convey a sense of relative value to other terms we’ve invented and which the audience also doesn’t recall. Using a specific generic term is convenient.
What about coins? Unlike with bills, each coin may have a name (penny, nickel, dime, and quarter) but they can all be referred to with the generic “cents.” And that’s exactly what people do. I might give someone “seventy-five cents,” not say that I gave them “three quarters.” Someone not familiar with the U.S. system can infer that a quarter is the one valued at 25 cents, but only because I specified that the three quarters amounted to seventy-five. By contrast, if I say I provided three nickels, do you know if that’s three times one ($.03), three times five ($.15), or three times ten ($.30)?
We don’t want to do this to an audience. Therefore, two generic words, such as “dollars” and “cents,” one denoting whole and another for part of a whole, provide a better sense of relative value and is preferred for fictional monetary systems. Avoid inventing names for denominations (i.e., “penny,” “dime”). If we really want to, we can, but use them wisely when writing. For example, “Seeing the price was fifteen cents, he pulled three nickels from a pocket.” Contrast that with, “Seeing the price, he pulled three nickels from a pocket.” The second tells us nothing about how much he’s paying unless we know the value of the denomination; our knowledge of it is required (italics) to understand. The first tells us what he’s paying, with a minor detail of how he did so as an option.
With this in mind, we can decide coins, gems, or bills have names and values but still default to generic terms like “dollars” and “cents” to indicate relative value, only rarely specifying which coins, gems, or bills someone used. Or we can just go with two generic terms and be done.