What is the difference between a red and brown dwarf?
A red dwarf is a low mass Star that fuse ordinary hydrogen like our Sun, but only at a very low rate. Brown dwarfs cannot fuse ordinary hydrogen but may fuse some other isotopes like deuterium.
Red dwarfs generally have between 7.5% and 50% of the Sun's mass. Sometimes slightly more massive stars are included, but our Sun is definitely too massive. None of these has more than one tenth the luminosity of the Sun, and with their very low rate of fuel consumption some smaller red dwarfs can shine on for trillions of years (our Sun will last a total of only about 10 billion years). Proximal Centauri, the nearest star outside our Sun at 4.2 light years away, is a red dwraf.
Brown dwarfs are distinguished by their inability to fuse ordinary hydrogen, but they can fuse some less abundant isotopes like deuterium and lithium. Brown dwarfs are far less luminous than even red dwarfs. They are considered "substellar objects" whereas red dwarfs are full stars. With their low luminosity and relatively low temperatures, brown dwarfs are more readily detected by infrared emissions instead of being seen visually, even with powerful telescopes. The nearest (known) brown dwarf is 6.5 light years away.