How are quasars different from regular galaxies?
Quasars are active galaxies.
A quasar is powered by a supermassive black hole at the centre of a galaxy. The black hole has a disc of material spiralling into it called an accretion disc. If material is constantly falling into the accretion disc it gets heated by friction and the gravity of the black hole to the point where it emits vast amounts of energy.
Many galaxies, including our own Milky Way galaxy, have supermassive black holes at their centres. So, it is possible that these "regular galaxies" were quasars in their youth. They would have stopped being quasars when the supply of material falling into the accretion disc ran out.
When two galaxies collide it is possible that a quasar can form. This could happen when the Milky Way and Andromeda galaxies collide in 3-5 billion years time.