Wisdom from the Early Stoics, Zeno of Citium 35

Genus (in logic) is the comprehension in one of a number of inseparable objects of thought: e.g. Animal; for this includes all particular animals.

A notion or object of thought is a presentation to the intellect, which though not really substance nor attribute is quasi-substance or quasi-attribute. Thus an image of a horse may rise before the mind, although there is no horse present.

Species is that which is comprehended under genus: thus Man is included under Animal. 

The highest or most universal genus is that which, being itself a genus, has no genus above: namely, reality or the real; and the lowest and most particular species is that which, being itself a species, has no species below it, e.g. Socrates. 

—Diogenes Laërtius, 7.60-61