leisure vs free time

leisure and free time both are nouns.

Word	Noun	Adjective	Verb	Adverb
leisure	Yes	No	No	No
free time	Yes	No	No	No

As nouns, free time is a hyponym of leisure; that is, free time is a word with a more specific, narrower meaning than leisure:

Other hyponyms of leisure include spare time, holiday, vacation, playday, playtime.

leisure (noun)	free time (noun)
freedom to choose a pastime or enjoyable activity	time that is free from duties or responsibilities
time available for ease and relaxation	time available for hobbies and other activities that you enjoy