I'm wondering if knowing the language Primordial means that you understand all different languages of elementals?
Yes, it does.
From the Languages section of "Chapter 4: Personality and Background" (PHB, p. 123):
Some of these languages are actually families of languages with many dialects. For example, the Primordial language includes the Auran, Aquan, Ignan, and Terran dialects, one for each of the four elemental planes. Creatures that speak different dialects of the same language can communicate with one another.