free rein vs freedom

free rein and freedom both are nouns.

Word	Noun	Adjective	Verb	Adverb
free rein	Yes	No	No	No
freedom	Yes	No	No	No

As nouns, freedom is a hypernym of free rein; that is, freedom is a word with a broader meaning than free rein:

free rein: the removal of constraints
freedom: the condition of being free; the power to act or speak or think without externally imposed restraints

free rein (noun)	freedom (noun)
the removal of constraints	the condition of being free; the power to act or speak or think without externally imposed restraints
	immunity from an obligation or duty