Postulates, as I understand them, are statements taken without proof, things that are assumed to be true. They are also called axioms. One example would be the axioms that, together with the undefined terms, form the basis for a geometry.
Conjectures are statements which have not yet been proved, but which are expected to be proved (or at least the attempt is expected to be made). They are also called hypotheses.
Hope that helps a bit.
Eliz.