All these terms refer to solidification and dispersion strengthening of alloys.
When the solubility of a metal is exceeded by adding too much of an alloying element, a second phase forms. As a result, a grain boundary between two phases is created. This boundary interferes with the slip of dislocations thereby strengthening the metal. In any dispersion-strengthened alloy, the continuous phase is known as the matrix. The second phase, typically present in smaller amounts, is called the precipitate.The precipitate acts as a strong obstacle to slip of dislocations in the matrix. These particles should be small and numerous to increase the likelihood that they interfere with the slip process. For this reason they are also called dispersoids in the sense that they are finely divided particles of one substance dispersed in another. On the other hand, intermetallics are compounds made up of two or more elements, producing a new phase with its own composition, crystal structure and properties. They are usually very hard and brittle, thus providing excellent dispersion strengthening of the softer matrix. Both stoichiometric and nonstoichiometric compounds can form. The former have a fixed composition (e.g. Fe3C in steels, Mg2Ca, AlSb) whilst the latter show a range of compositions (e.g. nickel aluminides, MoRh). These compounds have typically high melting points and can display desirable magnetic, superconducting and chemical properties. Intermetallics have given rise to several new materials developments. Some examples include hydrogen storage materials in nickel metal hydride (NiMH) batteries (see more details at: http://data.energizer.com/PDFs/nickelmetalhydride_appman.pdf).