They are not "earth magnets", they are "rare earth magnets". This describes the materials of which they are made. The elements are grouped into families with similar properties. These families have names. For example, the family containing helium, neon, argon, krypton, xenon, and radon is called the Noble Gasses. One of these families is the Rare Earths, which are group 3 on the periodic table. The rare earth elements most commonly used to make magnets are neodymium and samarium.
Common magnets are ferrites bound in either ceramic (rigid magnets) or rubber (flexible magnets). Rare earth magnets are much stronger for a given size/mass but also much more expensive (the 'rare' in the name is there for a reason - these elements are rare on the earth and therefore more costly than much more common things like iron ferrites).