1670s, "belonging to a large group of objects," formed in English from Latin gener-, stem of genus "race, kind" (from PIE root *gene- "give birth, beget," with derivatives referring to procreation and familial and tribal groups) + -ic. Hence "of a general kind, not special. In reference to manufactured products, "not special; not brand-name; in plain, cheap packaging," is from 1953 of drugs; of groceries, etc., from 1977. Related: Generically.
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