The very thin rim visible on one side of each "token" is a sign to me that they were punched-out of a sheet of metal - in effect, much the same as coin blanks are. THat they were not struck or anythgin after being punched out indicates they are either non-numismatic, or were done very cheaply. I think they are "supposed to be" blank and any shapes or patterns you're seeing on the "blanks" are just
Pareidolia. I agree that the characters on the painted one look "roughly Asian" but appear to be somewhat sloppily drawn - which would be unusual in a culture that prides itself on good calligraphy, which again tells me it was something done quickly, and perhaps not intended to be looked at as closely as we're now looking at them.
One possibility that fits all these criteria occurs to me - especially if they're in a group or set - is that they're "stage money", used as props in theatre plays or some such. All a "stage coin" has to be is round, shiny, and be made of metal so it makes a proper clinking sound when jingled or thrown around up on the stage. Using obviously-fake-up-close prop coins reduces the chances an impoverished actor would pocket the props for spending money.
Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis