There are many different types of candy mints, and many of them do not actually have real mint oil in them, rather they just have mint flavoring. Wintergreen, for example, is not actually mint, but only a type of flavoring. These flavorings are a part of candy mints, but are not actually from the biological family Mentha, the mint family.
Other classifications for mints include hard mints, soft mints, scotch mints, and mint imperials. Hard mints are what people generally think of when they think of mints: a hard mint used for freshening your breath, including brands like Altoids and Tic Tacs. Soft mints are made with a lot of butter so that they melt in your mouth.
Scotch mints are generally found in the United Kingdom and are round and have a hard shell, but a softer inside. Mint imperials are like scotch mints, except there inside is more crumbly than soft. Mint is also generally considered good for digestion. For this reason, it is not uncommon, nor a bad idea to drink mint tea after eating.