'aphyric-rhyolitic' is a compound formed from 'aphyric' + 'rhyolitic'. 'aphyric' is formed from the Greek prefix 'a-' meaning 'without' combined with 'phyric' (a petrological formation meaning 'having phenocrysts'), while 'rhyolitic' is the adjective of 'rhyolite', from New Latin/Germanic geological nomenclature.

'rhyolite' entered scientific use via German 'Rhyolith' in the 19th century (from elements of Greek 'rhyax' 'stream/flow' + 'lithos' 'stone') and gave rise to the adjective 'rhyolitic'. 'aphyric' is a more recent petrological coinage (20th century) combining the negative prefix 'a-' with 'phyric' to denote absence of phenocrysts; the compound adjective 'aphyric-rhyolitic' is used in modern geological descriptions.

Initially 'rhyolite' named rock associated with flow-like (stream) textures; over time it settled as the standard term for a high-silica volcanic rock. 'aphyric' has consistently meant 'without phenocrysts'; combined, the compound now denotes rhyolitic rock that is essentially crystal-poor.