The US has states because it is a federal country. Most countries are not federal so they are just countries with one government over the lot, not split into federal and state government. The minority of countries that actually ARE federal usually have some historical reason for it - I do know that with the USA, it started as various separately-founded colonies and when it came to declaring independence from the UK, obviously it made sense to band together to fight the British, but for other purposes, they wanted to stay separate and govern themselves their own individual way. And so it has been ever since. Good thing too when you consider the deep divisions between them on moral and social issues.
A couple of countries in Europe that actually ARE federal are Germany and Switzerland. Until 1871, Germany didn't exist - it was a collection of little principalities (so there are a lot of formerly royal families around there) so a lot of Germans (my best friend happens to be one) feel more attached to their former principality. So it just made sense to make Germany federal, even when it started all over again after the Second World War, and it has 16 states, each called a Land.
Switzerland is a collection of cantons and half-cantons because it's all mountains and in the past it was difficult to travel from one valley to the next, so they all had to run themselves and that has just hung on. It also explains why the Swiss German language varies a lot between them.
Incidentally, Switzerland has one of the world's purest forms of democracy. It is famously referendum-mad and a Swiss guy I know is forever getting a pile of ballot papers in the post every few months to vote on something or other. Anyone can call one if they get enough signatures to a petition. A recent controversial one was on whether to ban minarets on mosques, and knowing the Swiss, it doesn't surprise me that they voted for it. Cantons used to have a Landsgemeinde, an annual meeting of all citizens to elect the local council for the next year and make any laws they want, and the canton of Glarus and the half-canton of Appenzell-Innerrhoden still do. The rest have given up because the population got too big, but these two can still fit everyone into a local sports stadium and do it.
Don't mess with the Swiss. They require all young male citizens to do army service, and afterwards, to keep their army-issue weapon at home until the age of 30, taking it in every year to service it and make sure it hasn't been improperly used. To make that work, the Swiss need to be a self-disciplined lot and they most certainly are.
Other European countries are just countries. The geography of the Balkans has certainly changed since Yugoslavia fell to bits a little over 20 years ago. Under Marshal Tito, somehow it managed to stay together but when he died, it's all split up into Serbia, Croatia, Slovenia, Bosnia-Herzegovina and a few more.
You only 'cite sources' if you are doing an essay that the teacher assigned to you. Adults are out of school and don't need to do this.
All of the countries you list are both countries or sovereign states. The difference between the two terms is so obscure that most people use them interchangeably.
They are not provinces. Provinces are subunits of a country. Due to the history of the formation of the United States from multiple sovereign states, the terminology can be confusing, but the subunits of most countries are called provinces, but hte subunits of the United States are called states.
Subunits of countries can also be called cantons. We tend to use canton for very small units, and whether we call something a province or a canton is mostly historical. That is, you can't come up with a strict definition that explains when one term or the other would be used. Someone started using a term a long time ago for each province or canton, and the term stuck.
Providence is no a term used for this. It is a word that means "divine care". There is a city in the state of Rhode Island in the United States called Providence, but it is not a generic term for any governmental unit.
If you want to be very precise, not all the states of the United States are actually states. Some of them are technically Commonwealths. I'll let you google if you care about the difference, but I'll bet that most people in the United States are unaware of the difference because state has become the term used.
Oh dear, they are independent countries. LOOK AT A MAP!!!!!
They are called countries (because this is what they are)
