Hypothesis is a theory which can after testing be accepted or rejected. A hypothesis is a guess about the outcome of a certain set of conditions, usually, based on experience or observations. To test the hypothesis an experiment would be conducted. A hypothesis has some extra status in scientific discourse, in that scientists frequently put forward hypotheses they consider to be plausible, and perform tests to see whether they stand up to them.

A postulate is something that is assumed to be true without proof. Sometimes postulates are also called axioms.

I think it is no more than that 'hypothesis' comes from Greek, and 'postulate' comes from Latin. Generally we are supposed to test the 'null' hypothesis (i.e. the opposite of what we think might be the case), while a postulate is just an idea, but in practice I think these are just different words for the same thing.  We start with an idea, formalize it as a hypothesis (postulate), and then test the idea by experiments which progressively reduce the number of possible objections to the idea. At least, that's the way I go about it. We can make several hypotheses (postulates) based on 'the idea', all of which makes the process fun to do.

Hypothesis is a theory which can after testing be accepted or rejected. A hypothesis is a guess about the outcome of a certain set of conditions, usually, based on experience or observations. To test the hypothesis an experiment would be conducted. A hypothesis has some extra status in scientific discourse, in that scientists frequently put forward hypotheses they consider to be plausible, and perform tests to see whether they stand up to them.

A postulate is something that is assumed to be true without proof. Sometimes postulates are also called axioms.

Sometimes postulates are given as brain teasers.   The famous example is Euclid's 5th postulate (see attached image).    It was Janos Bolyai who introduced what he  called  imaginary geometry (also called hyperbolic geometry), which is a geometry of curved spaces on a saddle-shaped plane (see the attached image).   In such a space, the angles of a triangle do not add up to 180 degrees and the shortest distance between two points is a geodesic (curve), not a straight line.

http://www.robertnowlan.com/pdfs/Bolyai,%20Janos.pdf

Here is a brief history of the parallel postulate:

http://www.beva.org/math323/asgn6/nov19.htm

Postulates: Don’t they have kind of “pre-history” within a theory? I mean, in a sense that it is not arbitrarily said “lt should be like that”. Instead they follow from assumptions already made in the theory or made in the formulation of the problem. If this is true, then we do not start with them. During the process we might say “If we are to go on, we will need…” This can happen after some failures. Then postulates are both – first required and later on presupposed.

Hypothesis (Υπόθεσις) is a Greek word that means in many words: "let us suppose that...".

On the other hand, postulate in Greek is Axiom (Αξίωμα):

https://translate.google.com/#en/el/axiom

which is taken as valid and upon its validity we build a whole mathematical or physical structure.

Examples in Mathematics are Euclid's postulates that have built the linear geometry.

Examples in Physics are the two postulates, one that says speed of light is the same for a specific class of moving frames and leads to special relativity and a second that says you cannot distinguish between falling in a gravitational field and freely falling that leads to the general relativity theory.

A hypothesis explaining the mechanism by which prism shapes and crystallite orientation are determined in the enamel of mammalian teeth is based on the postulate that the ameloblasts produce a secretory force. Two corollaries of the postulate are 1, as a first approximation the cell membrane of the Tomes' process of an ameloblast acts passively with respect to the movement of materials across the cell membrane 2, the velocity of the cell membrane normal to its surface is directly related to its rate of secretion.

The postulate suggests that an ameloblast secretes a hexagonal rod of enamel precursor material in the direction of its long axis. This rod is sheared by the oblique movement of the ameloblast to the rod it secretes. A model has been constructed to demonstrate that shear of a closely packed system of hexagons produces shapes identical to 5 out of 6 basic mammalian prismatic structures. It is argued that enamel precursor material probably flows through the developing enamel. By combining with corollary 1 the flow suggested by the model it is demonstrated in the transverse plane of the tooth that crystallite orientation, the position of a prism sheath and the relationship of both to the Tomes' process of the ameloblast can be accurately predicted. By combining the analysis with corollary 2 the appearances in the longitudinal plane of a tooth can be predicted with the same accuracy. It is suggested that the accuracy of the predictions justifies the assumption of the postulate.

http://link.springer.com/article/10.1007/BF02017542

"Hypotesis" is the unproven theory, comes from the author intuition and vision.

"Postulat" is the statement, the theory is built upon.