Question

state the main differences between the moderate and extremist ideology and methods​

Answer 1

Moderate is an ideological category which designates a rejection of radical or extreme views, especially in regard to politics and religion. A moderate is considered someone occupying any mainstream position avoiding extreme views and major social change.

Extremism is "the quality or state of being extreme" or "the advocacy of extreme measures or views". The term is primarily used in a political or religious sense, to refer to an ideology that is considered (by the speaker or by some implied shared social consensus) to be far outside the mainstream attitudes of society.