A genus is what is predicated in what a thing is of a number of things exhibiting differences in kind. We should treat as predicates in what a thing is all such things as it would be appropriate to mention in reply to the question, What is the object in question?- as, for example, in the case of man, if asked that question, it is appropriate to say He is an animal. The question, Is one thing in the same genus as another or in a different one? is also a generic question- for a question of that kind as well falls under the same branch of inquiry as the genus- for having argued that animal is the genus of man, and likewise also of ox, we shall have argued that they are in the same genus- whereas if we show that it is the genus of the one but not of the other, we shall have argued that these things are not in the same genus.
Some things are different kinds of things. A book is a different kind of thing from a magazine. A genus collects a group of things that are different kinds of things and says that they are similar. For example, human beings and chimpanzees are both primates. This similarity can be spoken of as the kind of thing something is. So men and chimps are both primates. Any answer to the question What is it? when we are speaking about some kind of thing is a genus of that thing. The question Is one thing in the same genus as another or in a different one? is a question about genus. If we show that oxes and humans are the same kind of thing animals, then we have shown that they have the same genus. On the other hand, if we show that oxes are bovines while humans are primates, then we have shown that they are not in the same genus.
The problem with this description is really simple. We know that human beings are both primates and animals while oxes are both bovines and animals. So if genus refers to any kind of thing, then primates, bovines and animals are all genus. In that case, oxes and humans share the genus animal but do not share the genus primate or bovine. Perhaps Aristotle means to claim that the most specific genus possible must be shared in order to say that they have the same genus. In that case, bovines and primates may both be mammals, but oxes are humans are bovines and primates. This problem is not resolved in this passage.
Next Aristotle discusses the final category of topics: accidents.