South African vs Boer

South African and Boer both are nouns.

Word	Noun	Adjective	Verb	Adverb
South African	Yes	Yes	No	No
Boer	Yes	No	No	No

As nouns, Boer is a hyponym of South African; that is, Boer is a word with a more specific, narrower meaning than South African:

South African: a native or inhabitant of South Africa
Boer: a white native of Cape Province who is a descendant of Dutch settlers and who speaks Afrikaans

Other hyponyms of South African include Afrikander, Afrikaner.

South African (noun)	Boer (noun)
a native or inhabitant of South Africa	a white native of Cape Province who is a descendant of Dutch settlers and who speaks Afrikaans

South African (adjective)	Boer (adjective)
of or pertaining to or characteristic of South Africa or its people