Planetary mixers have an agitator that rotates on an axis as it moves throughout the mixing bowl in the same way the planets follow in their trip around the sun, hence the name. This type of mixer is designed for blending, mixing, chopping, and whipping ingredients, as it agitates the entire mixture more thoroughly than a spiral arm. If you're going to be mashing potatoes, whipping cream, or mixing ingredients, planetary mixers will perform better than spiral mixers.
Spiral mixers, on the other hand, have a single fixed arm that rotates throughout the mixing bowl. This arm is usually a spiral shape, which gives the mixer its name. The spiral arm has fewer moving parts than a planetary mixer, which means it has more strength to mix denser products. Spiral mixers are almost always used for kneading dough, so if you're running a bakery, pizzeria, or any other business that will be crafting a lot of bread, a spiral mixer is probably the best choice for you.