Final answer:
Brown dwarfs are substellar objects unable to sustain regular hydrogen fusion but can fuse deuterium, whereas red dwarfs are low-mass main sequence stars that undergo hydrogen fusion and are denser than the Sun.
Step-by-step explanation:
The key differences between brown dwarfs, red dwarfs, and other main sequence stars lie in their mass and the nuclear processes they are capable of. Brown dwarfs are substellar objects with masses from about 13 to 80 times that of Jupiter, which are not massive enough to sustain regular hydrogen fusion like main sequence stars but can fuse deuterium.
They are categorized by spectral classes of M6.5 and later and cool over time, transitioning from M to L, T, and Y spectral types. In comparison, red dwarfs are low-mass main sequence stars with a mass of around 1/12 that of the Sun, capable of sustaining hydrogen fusion, and have notably higher average densities than the Sun.