sabbatical vs leave of absence

sabbatical and leave of absence both are nouns.

Word	Noun	Adjective	Verb	Adverb
sabbatical	Yes	Yes	No	No
leave of absence	Yes	No	No	No

As nouns, leave of absence is a hypernym of sabbatical; that is, leave of absence is a word with a broader meaning than sabbatical:

sabbatical: a leave usually taken every seventh year
leave of absence: the period of time during which you are absent from work or duty

Other hypernyms of sabbatical include leave.

sabbatical (noun)	leave of absence (noun)
a leave usually taken every seventh year	the period of time during which you are absent from work or duty

sabbatical (adjective)	leave of absence (adjective)
of or relating to sabbatical leave
of or relating to the Sabbath