Jetons are common in Europe and chips are common in America. There's a reason for that, and it has to do with Poker (or perhaps even more importantly, the defunct game Faro).
The poker chips we know and love are descended from gaming tokens that have been used since ancient times. In Europe, Whist and some other related card games were often played for stakes, and counters were used to keep track of how many stakes each player owed. The counters came in various shapes and sizes (including, for reasons that elude me, counters shaped like fish).
These practices carried over into America as well, but in America something unique happened. America had a frontier. Frontiers are settled by the adventurous. And of the many sorts of adventurous people who expanded into the American west, among them came the professional gambler. And with the gambler came Faro, and then later Poker. Faro was directly imported from the French, but it became wildly successful in America; Poker, on the other hand, was a purely American novelty.
Faro and Poker have a difference from Whist and other card games played for stakes - they are inherently
gambling games, where money is the primary element, whereas in most other card games the players are merely wagering on the outcome, and the use of tokens is merely an aid to keep score. Faro and Poker both require placing actual money on the table... or they would, except using tokens as a substitute for money was a natural adaptation.
So while in Europe casinos were evolving games such as roulette and twenty-one, in the American west Faro and then later Poker were taking off. This led to two separate lines of development. In Europe, the fish-shaped counters, most commonly made out of mother-of-pearl imported from China, evolved into counters of different shapes and sizes to represent different values, and mother-of-pearl gave way to translucent plastics once plastics were created. In America, counters were made out of whatever was at hand - wood, ivory, and bone - and settled on a common shape and size (round) with colors and designs being used to distinguish different values. When the age of plastics arrived, blends of plastic and fillers such as clay and sawdust took over, but the familiar characteristics of roundness, opaqueness, and uniformity of size remained.
As to why you can sometimes find European jetons in American casinos... ¯\_(ツ)_/¯
Maybe next time someone's there they could ask the dealer.
