We do have the same meaning in English, but it's been obsolete for a while. From the Oxford English Dictionary: †2. a. A class of things or beings distinguish

We do have the same meaning in English, but it's been obsolete for a while. From the Oxford English Dictionary: †2. a. A class of things or beings distinguished by having certain characteristics in common; (as a mass noun) these regarded collectively; kind, sort. Obsolete. In earliest use: genus, as opposed to species (see note at genus n. 1).