The difference between Muster and Rally

Muster as a noun (chiefly, _, military):

Gathering. An assemblage or display; a gathering, collection of people or things. An assembling or review of troops, as for parade, verification of numbers, inspection, exercise, or introduction into service. The sum total of an army when assembled for review and inspection; the whole number of effective men in an army. A roundup of livestock for inspection, branding, drenching, shearing etc.

Muster as a noun (obsolete):

Showing. Something shown for imitation; a pattern. An act of showing something; a display. A collection of peafowl (an invented term rather than one used by zoologists).

Muster as a verb (transitive, obsolete):

To show, exhibit.

Muster as a verb (intransitive):

To be gathered together for parade, inspection, exercise, or the like (especially of a military force); to come together as parts of a force or body.

Muster as a verb (transitive):

To collect, call or assemble together, such as troops or a group for inspection, orders, display etc.

Muster as a verb (transitive, US):

To enroll (into service).

Muster as a verb (transitive, Australia, New Zealand):

To gather or round up livestock.

Rally as a noun:

A demonstration; an event where people gather together to protest for or against a given cause

Rally as a noun (squash, table tennis, tennis, badminton):

A sequence of strokes between serving and scoring a point.

Rally as a noun (motor racing):

An event in which competitors drive through a series of timed special stages at intervals. The winner is the driver who completes all stages with the shortest cumulative time.

Rally as a noun (business, trading):

A recovery after a decline in prices (said of the market, stocks, etc.)

Rally as a verb:

To collect, and reduce to order, as troops dispersed or thrown into confusion; to gather again; to reunite.

Rally as a verb:

To come into orderly arrangement; to renew order, or united effort, as troops scattered or put to flight; to assemble; to unite.

Rally as a verb:

To collect one's vital powers or forces; to regain health or consciousness; to recuperate.

Rally as a verb (business, trading):

To recover strength after a decline in prices; -- said of the market, stocks, etc.

Rally as a verb (transitive):

To tease; to chaff good-humouredly.

Rally as a noun:

Good-humoured raillery.