A starburst galaxy is a galaxy forming stars at a very high rate (undergoing a starburst), i.e., so high that all its gas would be gone if this had been going on for the life of the galaxy. The Milky Way which is not a starburst galaxy is estimated to produce about one Sun per year.
Star formation can be indicated by strength in the spectrum of hot, young stars, which are necessarily recent, but many of the young stars are hidden by the dust clouds that were their origin, and are detected by infrared radiation reradiated from these clouds.
It is thought that mergers and close encounters between galaxies causes them to start forming lots of stars. There is evidence that they can form so many stars so close together that a gas blowout results from the pressure, resulting in a quenched galaxy, i.e., with little star formation.
The term quiescent, as in quiescent galaxy can refer to a galaxy that is not starburst, or in context, it can refer to a galaxy that isn't forming stars at all, i.e., not a star forming galaxy (i.e., SFG).