Rebel, insurgent, iconoclast are comparable when they denote one who rises up against constituted authority or the established order.
Rebel carries the strongest implication of a refusal to obey or to accept dictation and of actual, often armed, resistance to what one opposes; the term does not necessarily imply antagonism to a government but is comprehensive enough to cover one who defies a generally accepted authority (as of a law, a tradition, or a custom).
Insurgent applies chiefly to a rebel who rises in revolt but who is not regarded by the authorities as having the status of an enemy or belligerent; thus, rebels in a colony or dependency of an empire may, from the imperial point of view, be designated as insurgents, even though they call themselves rebels .
In a more extended use insurgent applies to a rebel (as in a political party, a church, or a group of artists or writers) who rises in revolt not so much in an attempt to destroy the organization or institution or its laws or conventions as in the hope of effecting changes or reforms believed to be necessary.
Iconoclast, historically applicable to one of a party of insurgents in the Eastern Church in the 8th and 9th centuries who opposed the use of images, is applied in an extended sense to a person who, especially in the capacity of a reformer, violently attacks an established belief, custom, tradition, or institution.