cinnamon bark

A collection of cassias
Broadly speaking there are two types of cinnamon that we use in America: Ceylon cinnamon and cassia cinnamon. The most common is cassia, which itself can be divided into three different kinds depending on origin: Korintje from Indonesia (Cinnamomum burmannii), Saigon from Vietnam (Cinnamomum loureiroi), and somewhat confusingly, cassia from China (Cinnamomum cassia). These three are largely similar enough in taste and aroma that they have been roughly grouped under the name cassia.

Also known as
It's worth noting, that matters are further confused as these three cassias might go by different common name monikers; Korintje can be called Indonesian cinnamon, Saigon can be called Vietnamese cinnamon or Vietnamese cassia; and cassia can be called Chinese cinnamon.

Cinnamon truths
The other main type of cinnamon is Cinnamomum verum called Ceylon cinnamon, true cinnamon, or sometimes Mexican cinnamon. It is what is primarily sold in Europe and in Mexico (as canela) for cinnamon. It is more a more subtle and will yield a different taste if substituted. It is more expensive than the cassia types and is marked for having a very low coumarin content.