brain wave vs beta wave

brain wave and beta wave both are nouns.

Word	Noun	Adjective	Verb	Adverb
brain wave	Yes	No	No	No
beta wave	Yes	No	No	No

As nouns, beta wave is a hyponym of brain wave; that is, beta wave is a word with a more specific, narrower meaning than brain wave:

brain wave: (neurophysiology) rapid fluctuations of voltage between parts of the cerebral cortex that are detectable with an electroencephalograph
beta wave: the normal brainwave in the encephalogram of a person who is awake and alert; occurs with a frequency between 12 and 30 hertz

Other hyponyms of brain wave include alpha rhythm, alpha wave, beta rhythm, delta rhythm, delta wave, theta rhythm, theta wave.

brain wave (noun)	beta wave (noun)
(neurophysiology) rapid fluctuations of voltage between parts of the cerebral cortex that are detectable with an electroencephalograph	the normal brainwave in the encephalogram of a person who is awake and alert; occurs with a frequency between 12 and 30 hertz