First things first, neutron stars, quark stars and black holes are all born via the same mechanism: a supernova. But each of the three are progressively more massive, so they originate from supernovae produced by progressively more massive stars.
So, what if a star exploded, producing something a little too massive to be called a neutron star? Well, neutron stars resist collapsing under their own gravitational pull by a characteristic of matter known as neutron degeneracy. This produces an outward force called neutron degeneracy pressure.
What if the neutron star born after a supernova is too massive for this neutron degeneracy pressure to hold up against the neutron star's own gravity?
In this case, it's up to the quarks that make up the neutrons to take over, preventing the body from collapsing any further. Single neutrons are composed of three quarks (two "down" quarks and one "up" quark).
When quark degeneracy pressure kicks in, a quark star may be produced; the free "up" and "down" quarks get converted into "strange" quarks. Therefore, a quark star (also known as a "strange star") is made up of strange matter.
