Strange matter is a particular form of quark matter, usually thought of as a "liquid" of up, down and strange quarks. It is to be contrasted with nuclear matter, which is a liquid of neutrons and protons (which themselves are built out of up and down quarks), and with non-strange quark matter, which is a quark liquid containing only up and down quarks. At high enough density, strange matter is expected to be color superconducting. Strange matter is hypothesized to occur in the core of neutron stars, or, more speculatively, as isolated droplets that may vary in size from femtometers (strangelets) to kilometers (quark stars).
In particle physics and astrophysics, the term is used in two ways, one broader and the other more specific
Under the broader definition, strange matter might occur inside neutron stars, if the pressure at their core is high enough (i.e. above the critical pressure). At the sort of densities we expect in the center of a neutron star, the quark matter would probably be strange matter. It could conceivably be non-strange quark matter, if the effective mass of the strange quark were too high. Charm and heavier quarks would only occur at much higher densities.
A neutron star with a quark matter core is often called a hybrid star. However, it is hard to know whether hybrid stars really exist in nature because physicists currently have little idea of the likely value of the critical pressure or density. It seems plausible that the transition to quark matter will already have occurred when the separation between the nucleons becomes much smaller than their size, so the critical density must be less than about 100 times nuclear saturation density. But a more precise estimate is not yet available, because the strong interaction that governs the behavior of quarks is mathematically intractable, and numerical calculations using lattice QCD are currently blocked by the fermion sign problem.