Video Games Encyclopedia

The run-and-gun platform genre was popularised by Konami’s Contra. Among the most popular games in this style are Gunstar Heroes and Metal Slug. Side-scrolling run-and-gun games marry platformers with shoot ’em ups, with less tricky platforming and more shooting. These games are sometimes called platform shooters. The genre has arcade roots, so these games are generally linear and difficult.
There are games which have a lot of shooting but do not fall in this subgenre. Mega Man, Metroid, Ghosts ‘n Goblins, Vectorman, Jazz Jackrabbit, Earthworm Jim, Turrican, Cuphead and Enchanted Portals are all platformers with shooting, but unlike Contra or Metal Slug, platforming, as well as exploring and back-tracking, figures prominently. Run-and-gun games are generally pure, and while they may have vehicular sequences or other shifts in style, they have shooting throughout.

Reference: Wikipedia