There are many coin collecting themes and often combined together, like collecting by countries, years, mint marks, compositions, subjects, periods, values.
Our coin sets collections consist of major design variants for a period of time in one country. There may be coins of various designs in the same numismatic period.
What is the numismatic period? Coins and paper money consists of unique symbols, designs and themes based on the country's economical, political or social situation. Each country has its own history and traditions and it may be visible on the currency. Some countries had wars, economical and political crises, changes of the rulers (Kings, Queens, Dictators), some had changed the status of a country (e.g. from a monarchy to a republic) and some were not affected by the world situation.
The U.S. is fortunate that there have been no terrible events in its history and you can see that this country doesn't have what we call "coin sets".
The best example is Switzerland. Swiss coins are identical as were circulated in 1850. In 1968 they have changed the composition from silver to copper-nickel clad.
The United Kingdom has Her Majesty Queen Elizabeth II which is showing on every single coin from 1953 to now. They do have coin sets even if the numismatic period is the same (Pound). There are 5 different coin versions with a portrait of a queen, from very young to old aged.
Brazil is one of the countries that has changed currency 7 times in the 20 century. I don't know what's happened there but they used these currencies: Reis until 1942, then Cruzeiros until 1986, Cruzados until 1988, Cruzado Novo for one year, and then Cruzeiro until 1993, and finally Cruzeiro Reals until now. All coins had different numismatic values, symbols, and designs. That's a rich country with many different coin sets.
Some countries were occupied by the Soviets and they lost their own currencies, like the Baltic states (Lithuania, Latvia, Estonia) and 11 other countries. Even Germany was divided into two parts (East and West) and they had two different currencies.
Mostly of European countries were involved in WW2 and the coins made during the world was looks different because copper, Brass, or bronze was replaced by cheaper compositions. Bombs were priority no. 1 and that was reflected on the coins made with aluminum or zinc.