As evinced by counting their frequency on Usenet, "Doom clone" was a more common term than "first-person shooter" until the late 1990s.
Doom clones are games that mimic Doom's gameplay. In other words, most early first-person shooters — due to Doom's popularity, a huge number of such games appeared soon after its release. The term "Doom clone" was in fact the common term for first-person shooters until the late 1990s.
Among games often counted as Doom clones are those based on the Doom engine, such as Heretic and Hexen (see Games for more). Others include Rise of the Triad, Dark Forces, and Duke Nukem 3D.