From Teflpedia

Formally "America" is used in the sentences "North America", "South America", "Central America", "Latin America" and "the United States of America".

Geographically there are two continents which are called collectively "the Americas", and they are North America and South America. North America includes Central America and the Caribbean.

Sometimes the term "America" is used as a synonym of "the Americas".

Informally in English "America" is short for and means the United States of America. This usage is perceived as ethnocentric by residents of other North American and South American countries and some European countries as it confuses the name of the continent with that of one particular nation. To understand the feelings of people who are not American citizens you can see the Wikipedia talk pages of the article America (disambiguation).[1] Since it is an informal term which is very loaded in some places, it is better not to use the isolated word "America" in a class of English as a foreign language, particularly in Latin America.

The term "Latin America" refers to the countries of the Americas where Romance languages predominate, ie from and including Mexico in North America all the way to Cape Horn at the southern end of South America. Quebec is not considered part of Latin America, but Haiti is.

American English is the form of English common in the United States of America while Canadian English is spoken in Canada.

Wiktionary has a good definition of America.[2]