Strange matter, or strange quark matter, is quark matter containing strange quarks. In Nature, 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, as in the hypothetical strange stars. At high enough density, strange matter is expected to be colour superconducting.
Ordinary matter, also referred to as atomic matter, is composed of atoms, with nearly all matter concentrated in the atomic nuclei. The nuclear matter is a liquid composed of neutrons and protons, and they are themselves composed of up and down quarks. Quark matter is a condensed form of matter composed entirely of quarks. If quark matter contains strange quarks, it is often called strange matter (or strange quark matter), and when quark matter does not contain strange quarks, it is sometimes referred to as non-strange quark matter.
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 and high pressures 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 quarks 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.
One major area of activity in neutron star physics is the attempt to find observable signatures by which we could tell, from earth based observations of neutron stars, whether they have quark matter (probably strange matter) in their core.
If the "strange matter hypothesis" is true then nuclear matter is metastable against decaying into strange matter. The lifetime for spontaneous decay is very long, so we do not see this decay process happening around us. However, under this hypothesis there should be strange matter in the universe: