The terms ' genus ' and ' difference ' are, as has been said, terms of second intention. They symbolize two classes of terms (not two classes of things), distinguished by two ways of predication (viz., praedicare in quid, and respectively praedicare in quale quid, see Part III, VIA PRAEDICATIONIS, b. ways of predication ).
Every term belonging (on the basis of the present predicational context) in the box ' genus ' is an instance of it.
Every term belonging (on the basis of the present predicational context) in the box ' difference ' is an instance of it.
An instance of the term ' genus ' is, for example, the term ' animal ' (when figuring in ' man is an animal ' ), while an instance of the term ' difference ' is the term ' rational ' (when figuring in ' man is rational ' ).
When we say " man is an animal " we mean that man is a species of the genus animal. Here ' man ' stands for : Socrates, Plato, Peter, etc., that is, it stands for the species, and the proposition says that it is a species of the genus animal. It reveals part of the Essence of man. In the same way " man is rational " reveals part of the Essence of man.
On the other hand, if these terms figure in the corresponding definition, then the proposition says something of a term, namely the term ' man ' . It analyzes the term, that is, it defines the term. In this case we'd better leave out the article 'an', and say : man is animal, which predicates a partial definition of the term ' man '. The complete definition is predicated as follows : ' man ' is ' rational animal ', in the sense of : the term ' man ' means (that for which the term) ' rational animal ' stands (instead of predicating : man is a rational animal ), that is : the term ' man ' is defined by the term ' rational animal ' .
In the first case we said something about the essence of real beings like Socrates, Plato, Peter, etc., while in the second case we defined the term ' man '.