A Beastmaster (homebrew class) has both an animal familiar and a companion. My question is, what is the difference? I've looked them over and can't find any.
The most notable difference between animal familiars and companions is that the familiar can not directly attack. See the evolution section of the link you provided and note:
At level 5, the familiar may take evolution points from the companion's evolution to use on themselves. The familiar can only take evolutions that it meets the prerequisites for. Remember, the familiar CANNOT attack.
Also note the hit dice calculations. Your familiar has half your hit points rounded down, and your companion uses whatever hit dice are listed in their monster manual entry.