radical vs extremist

radical and extremist both are nouns.

Word	Noun	Adjective	Verb	Adverb
radical	Yes	Yes	No	No
extremist	Yes	Yes	No	No

As adjectives, radical and extremist are synonyms defined as:

radical and extremist: (used of opinions and actions) far beyond the norm

Other synonyms of radical include ultra.

As nouns, extremist is a hyponym of radical; that is, extremist is a word with a more specific, narrower meaning than radical:

radical (noun)	extremist (noun)
a character conveying the lexical meaning of a logogram	a person who holds extreme views
(linguistics) the form of a word after all affixes are removed
a person who has radical ideas or opinions
(mathematics) a quantity expressed as the root of another quantity
(chemistry) two or more atoms bound together as a single unit and forming part of a molecule
an atom or group of atoms with at least one unpaired electron; in the body it is usually an oxygen molecule that has lost an electron and will stabilize itself by stealing an electron from a nearby molecule

radical (adjective)	extremist (adjective)
especially of leaves; located at the base of a plant or stem; especially arising directly from the root or rootstock or a root-like stem	(used of opinions and actions) far beyond the norm
of or relating to or constituting a linguistic root
arising from or going to the root or source
(used of opinions and actions) far beyond the norm
markedly new or introducing radical change