A "complete list of countries" is a surprisingly difficult object to find. That's why every "list of countries" you might find on the Internet - or even on the coin forums - will be slightly different.
What, exactly, is a "country"? What do you include on the list, and what don't you? Do you include rebel/secessionist states? And as a coin collector, we deal with historic objects; it is not hard to obtain coins issued by countries that no longer exist or have significantly changed form since the coin was issued. What do you do with those? Coins go back a long, long time - before the invention of the "country" in the modern sense. What do you do with ancient Greek city-state coinages, or coins from German feudal states - does every single one of them count as a separate "country"? There were thousands of each of them.
The CIA Factbook list (and the Wikipedia list that uses the same data) is a list of all currently existing officially recognized countries, de-facto independent countries and dependent states; not all of these issue their own coins, so the list will have to be modified to exclude those. The Numista list is an attempt (albeit an incomplete one) to list all countries and other coin-issuing entities that have ever issued a coin.
In short, a "list of countries" can be as long or as short as you want it to be. If your intent is to make a list that you consider an achievable "goal" to aim to "complete", then you probably want to consider a list that's as short and simple as possible. Personally, I consider my "list of countries" as a journey, not a destination; it is always expanding as I buy new coins from places I've never heard of before.
