Middle English fom, fome (c. 1300), from Old English fam "foam, saliva froth; sea," from West Germanic *faimo- (source also of Old High German veim, German Feim), from PIE root *(s)poi-mo- "foam, froth" (source also of Sanskrit phenah; Latin pumex "pumice," spuma "foam;" Old Church Slavonic pena "foam;" Lithuanian spainė "a streak of foam"). The plastic variety used in packaging, etc., so called from 1937.
"type of volcanic rock having a loose or cellular structure," formerly used to smooth parchment or vellum, c. 1400, pomis, from Anglo-French and Old French pomis (13c.), from Late Latin pomicem (nominative pomex, genitive pumicis), from Oscan *poimex or some other dialectal variant of Latin pumex "pumice." This word is from PIE *(s)poi-mo-, a root with connotations of "foam, froth" (see foam (n.)), perhaps because pumice resembled a sort of fossilized foam.
With a wide variety of forms in Middle English, including pumish, pumey. Old English had pumic-stan. As a verb, "to polish or smooth with pumice," early 15c., from the noun.