No, they are not. A white dwarf is an entirely different thing from a dwarf star. Red (type M) dwarfs and yellow (type G) dwarfs are in the main sequence -- that is, they're still fusing hydrogen, and have plenty of it left to spare. A white dwarf is what remains after a star of a certain size (such as our yellow dwarf sun, Sol) has used up all its fuel and has become a tightly-packed globe of slowly-cooling, degenerate matter. It is, in essence, the corpse of an ordinary star.
White dwarfs are also much smaller and denser than any main sequence dwarf star; Proxima Centauri (a fairly typical red dwarf star) is at least half again as large as Jupiter, while your average white dwarf is barely larger than our own Earth.
Our current understanding of stellar evolution has red dwarfs eventually turning into white dwarfs too, but we have no proof of this because it is frankly impossible for them to exist yet. Red dwarfs burn their fuel so slowly that even the largest of them will have enough fuel to remain in the main sequence for hundreds of billions of years -- or many, many times longer than the current age of the universe. That the LBB6 tables create M-based white dwarfs so readily is IMHO the biggest clunker of that generation system.