In spite of their name, most of the 17 rare earth elements or metals aren't actually rare. The only unusual one is promethium, while others such as cerium are in fact among the more common elements. However, they are thought of as rare because, although there may be plenty of the elements worldwide, they aren't usually found in high concentrations. As it is expensive and difficult to exploit raw materials (through mining etc) those that are only found in small individual amounts are often not commercially worth using.

Those deposits of rare earth elements that do occur naturally in amounts large enough to exploit are known as rare earth minerals (minerals used sometimes to be called 'earths', hence the name.) So, a rare earth mineral consists mainly of one of more of the 17 rare earth metals.

You can find an overview of the facts about rare earth minerals here.