Type Ia supernovae are also known as thermonuclear supernovae. They involve a binary (or double) star system. Where one star is a white dwarf, and the other is usually a star like our Sun or a huge red giant star.
Brown dwarfs are very dim, glowing objects that never gained enough mass to become fully fledged stars. In other words, the temperatures and pressures at their centres never got high enough for nuclear fusion to start.