Based on the electronic layer structure and physicochemical properties of rare earth elements, as well as their coexistence in minerals and the characteristics of different properties that can be produced by different ion radii, the seventeen rare earth elements are usually divided into two groups:

Light rare earths include: lanthanum, cerium, praseodymium, neodymium, promethium, samarium, europium.

Heavy rare earths include gadolinium, terbium, dysprosium, holmium, erbium, thulium, ytterbium, lutetium, scandium, and yttrium. [1] 

Classified by mineral characteristics:

Cerium group (light rare earths) - lanthanum, cerium, praseodymium, neodymium, promethium, samarium, and europium;

Yttrium group (heavy rare earths) - gadolinium, terbium, dysprosium, holmium, erbium, thulium, ytterbium, lutetium, and scandium. [2] 

Classified by extraction and separation:

Light rare earths (P204 weakly acidic extraction) - lanthanum, cerium, praseodymium, neodymium;

Rare earth elements (P204 low acidity extraction) - samarium, europium, gadolinium, terbium, and dysprosium;

Heavy rare earths (P204 acidity extraction) - holmium, erbium, thulium, ytterbium, lutetium, yttrium.