A helium flash is the rapid fusion of helium in a star, fast enough to cease or subside very soon. It is a brief helium runaway, the fusion's generated heat contributing to more fusion.
A helium core flash (aka just core flash) is such fusion triggered when the core of an RGB star becomes degenerate (which happens when the mass is less than about two solar mass) and then becomes sufficiently hot and dense. (If the star is more massive, fusion begins before degeneracy takes hold, the added pressure from the heat limiting the density, a factor keeping the fusion from running away.)
A helium shell flash is such fusion in a shell-shaped region surrounding the core of an AGB star, when it gains sufficient helium and heat. In this case, the helium is from a surrounding shell of hydrogen fusion, and the helium fusion can occur periodically in such bursts.