In pre-Chassidic terminology, these parties are traditionally known as the Evil Inclination and the Good Inclination. However, Chassidus often also refers to these respective forces as the Nefesh Ha’Behamis, the Animal Soul, and the Nefesh Ha’Elokis, the Divine Soul. If in fact these terms are synonymous, why are additional terms needed?
The answer is that Chassidus, devoted as it is to explaining the inner workings of the soul, seeks to be more precise by adding additional terms in order to refer to different subparts of the same general soul entity. These subparts are the complementary intellectual and emotional elements of the respective souls:
Divine Soul: This refers specifically to the aspect of intellect that has a natural affinity for grasping G–dliness.
Good Inclination: This refers to this soul’s emotions, which consist primarily of love and awe of Hashem.
Animal Soul: This refers to the intellect of the Evil Inclination, which naturally grasps the pleasure of selfish instincts and lusts, and provides the person with the knowhow to satisfy these instincts. In this respect its intellect is animal-like, for an animal too uses its intellect to secure its survival, as it is written, “The ox knows its master, and the mule, its feeding trough” [Yeshaya 1:3]. Similarly, the animalistic intellect grasps the pleasure of selfish instincts and lusts, and provides the person with clever schemes in his quest to indulge in his lusts and commit sins and crime. Concerning this it is said, “They are shrewd to do evil” [Yirmiyahu 4:22].
Evil Inclination: This refers to this soul’s emotions, such as the desire for the physical, the fear of bodily harm, and the like. In the animal soul, the emotions are primary.
Although both souls contain intellect and emotions, they differ in terms of which of the two soul-powers is primary:
The Divine Soul is compared to a human, in which the intellect dominates (or at least ought to dominate) over the emotions. Thus, in the Divine Soul, the intellect is dominant and primary, while the emotions are subordinate to the intellect, and thus secondary.
In contrast, the Animal Soul is likened to an animal (hence the name), whose intellect is entirely subordinate to its instincts and emotions. Thus, just as an animal may be very intelligent, such as a fox, the most clever of the animals, its intellect can only be used to satiate its desires and instincts. Likewise, no matter how highly the intellect of the Animal Soul may be developed, it will use that force as a tool to pursue self-interest, and it will never be able to attain true impartiality and objectivity.
Torah Ohr, 38b.