The uncertain resemblance between Iapetus and the biblical Japheth, dismissed by modern linguists as a coincidence of sound, nonetheless had a real and significant career in the history of linguistic classification before that dismissal became settled scholarly consensus. In the eighteenth and early nineteenth centuries, well before the term Indo-European was established, some European scholars grouped the languages of Europe, and sometimes the wider family later called Indo-European, under the label Japhetic or Iapetic, drawing directly on the old idea that Japheth, son of Noah, was the biblical ancestor of the peoples of Europe, and reaching for Iapetus's name as its classical mirror. The label survived far longer than that shaky foundation might suggest: in the early twentieth century the Soviet linguist Nikolai Marr revived and radically reworked the term into his so called Japhetic theory, an ambitious and eventually thoroughly discredited proposal that treated Caucasian languages, and at various points nearly every other language family, as originally related stages of one evolving linguistic substance, a theory that enjoyed official favor in the Soviet Union for a time before being officially repudiated by Soviet linguistics itself in 1950.
Iapetus himself has no connection whatsoever to any of this beyond the accident of a name that sounded, to early modern ears steeped in the Bible and the classics alike, close enough to Japheth to seem meaningful. The episode is a useful caution about how quickly a plausible sounding etymology, even one classical scholars themselves eventually rejected, can escape its origin and shape entire fields of inquiry for generations before the resemblance is finally recognized as coincidence rather than kinship.