So is Balance magic like "earth" magic or geomancy? Because it has a desert themed style compared to other schools. Or is it just Desert magic? Just curious.
According to the Wizard101 website, Balance "draws on elements from each of the other schools." So it's not really specifically earth magic. The desert theme comes from the fact that Balance magic originates in Krokotopia, which is a desert themed world if you have not reached it yet. This is just for early spells, as later spells aren't really related to the desert at all. Take Hydra for example, which doesn't resemble the desert at all. Hydra is one of the unique features of Balance, as it attacks with ice, fire, and storm damage instead of balance, showing how Balance is meant to bring different schools together.
Balance is the incorporation of all magic so it has a little bit of everything
Exactly. Notice spells like spectral blast, hydra, chimera, ect. It uses other elements. Why do you think it's blades and traps are for any school? There are no balance shields or balance traps. It balances out all of the elements in one school.