In this chapter the Alter Rebbe explains the types of Righteous Ones (tzaddikim) which he mentioned in chapter 1 (the Righteous One who prospers and the Righteous One who suffers) and relates them to another phrase from our sages1 where they talk about a complete Righteous person as well as an incomplete Righteous person.
But how many types of Righteous Ones there are! The key is to understand that each of these Righteous Ones has two names. They are two Righteous Ones, with two names each: four names in total.
When a person strengthens their Divine Soul and fights against their Animal Soul so much that they drive it out of its place (on the left side of the heart), but do not transform it into good, this is called
1) Just incomplete.
2) Just the one who's doing badly.
Why does it have two names? Because one refers to the love of Hashem that this Righteous One has. This Righteous One still has some evil within him, and that means he does not love Hashem Completely, because if he loved only Him, there would be no evil within him. That is why he is an incomplete Righteous One, because what is incomplete is precisely his love for Hashem. This also means that his hatred of evil is incomplete… he still retains some appreciation for the passions and things of the material world.
The Alter Rebbe explains that love and hate are opposites, so if we love something intensely, we intensely hate its opposite. For example, if we love being alive, we will hate anything that causes death. The feeling of love for life will be as strong as the feeling of hatred for death.
The other name, Righteous One Who Fails, refers to the evil within him, which, despite being minuscule, almost as if it weren't there, is still present… it hasn't left nor has it ascended to Sainthood; it continues to receive vitality from the “Shining Shell.” That is why we say that “the evil” “is his” (in Hebrew, “tzadik veRá lo”which can be translated as that evil is “from him”), this Righteous One rules over his evil side, but he did not manage to cast it out or change it to good.
(But let's pay attention: Because the idea of "doing well" doesn't mean having money or health, as people usually describe someone "who is doing well." These ways of referring to people, like "Righteous One Who Is Doing Well" or "Wicked One Who Is Doing Well," are ways of identifying how much of the good they have revealed within their lives. That is, it's a way of expressing the relationship between the Divine Soul and the Animal Soul. When we say that someone "is doing well," it means that their Divine Soul is stronger than their Animal Soul, and when we say that someone "is doing badly," it means the opposite: that their Animal Soul is stronger than their Divine Soul.)
There are many levels of this kind of "Just to the one who's doing badly" that depend on how much he loves Hashem and how much he hates evil. That is why our wise men2 They say there are many Righteous people in the world, but they are of this type, incomplete.
The other righteous one also has two names,
1) Just right.
2) Just the one who is doing well.
This is a Righteous One who worked so hard on himself that he managed to transform his "inclination to evil" into an "inclination to good." This Righteous One loves so much Hashem And he hates evil so much that his evil side was transformed into good. There are very few righteous people like him, because it is a very high spiritual level.
At the end of the chapter, the Alter Rebbe explains that the completely Righteous One does not love Hashem because there will be a benefit in loving Hashem, like someone doing a favor for a reward, but only thinking about what Hashem He wants it, even if he understands that he will not benefit from it, and is ready to do anything to bring pleasure to Hashem. That is why he is also called pious (Hasid), who does not seek his own benefit, but the benefit of others.
1Talmud Berakhot 7a
2Talmud Sukkah 45b, Sanhedrin 97b