Illustration of a proton and a neutron. A proton is built up by three quarks, two up quarks and one down quark. A neutron is built up by three quarks as well, one up and two down quarks.
A neutron star consist of neutrons, which in turn is built up by quarks. The quarks are confined in the neutrons. In a quark star the quarks are deconfined, that is they are free particles that are not confined in nucleons. In addition, quark stars also include the strange quark.