A blackhole is the result of mass becoming so dense that the gravity crushes it into something incredibly tiny or perhaps even into a singularity. But BHs can grow by colliding with other masses. The center of most, if not all, galaxies has SMBHs (Super Massive Black Holes).
Quasars are visible in the electromagnetic spectrum. Black holes are not.
A quasar is a supermassive black hole at the center of a galaxy that has a huge amount of mass falling into it, like a steady diet of stars. This infalling matter heats up and radiates fiercely, which is what we see as a quasar, a BIG source of radiation far away.