There is a difference between חלב and שומן (fat): חלב is distinguished from meat, both in its nature and in its matter. And they will not get mixed together, since חלבis spread out loosely and has a membrane that can easily be peeled. And it will cluster on the sides as well. And the Torah explicitly restricts it from being sacrificed and being eaten.

And as a borrowed word, it will also call the fat of the tail fat of a sheep חלב, in that it is the best. And any place where the noun חלב comes where it means it is the best, it will come with a pronoun or in construct state. And the tail fat is called חלב for the purpose of a homiletical interpretation. Thus, with types of sin offerings, it is written כחלב זבח השלמים (as the fat of the sacrifice of peace-offerings)⁶⁸⁸.

footnotes: ⁶⁸⁸ Leviticus 4:26.