The phrase "generic sense" refers to something that is understood or used in a general or widespread way, without specific or unique qualities. It is a broad or common understanding of something. Full definition
In its most generic sense, the word earthquake is used to describe any seismic event — whether a natural phenomenon or an event caused by humans — that generates seismic waves. (newworldencyclopedia.org)
Thomas's reply is that something can be a certain something in two ways: either as a complete subsistent individual of a species (as Socrates is of the species man), or in a more generic sense that does not exclude parts, incomplete as they may be, from subsistence. (faith.org.uk)
Reagan's religious understanding is, in short, sectlike, in Ernst Troeltsch's generic sense of sects as one legitimate expression of the Christian gospel and tradition, and as one deep - rooted mode of American Christianity. (religion-online.org)