The term "American" can refer either to a person of one of the nations of the Americas or to a citizen of the United States. In English, the term American is the most common and correct way to refer to a US citizen despite the linguistic ambiguity.

I know several people from Spanish speaking countries who refer to themselves as "Americans" when speaking English in order to differentiate themselves from Europeans. This is mainly a failing of the English language, or possibly because the USA just needs to get a proper bloody name.

Other languages (French comes immediately to mind) use cognates to refer to Americans while other languages such as Spanish use terms referring to the United States to refer to US citizens. For example, in Spanish if you wanted to refer to someone or thing from the New World it would be "americano" someone from North America would be "norteamericano" while a US citizen would be "estadounidense".