Nominative Iōn, Genitive Iōn-os, Adjective Iōn-ikos or Iōn-ios refers to the tribe of Ionians.
Adjective Iŏn-ios refers to the sea, and is traditionally derived from the lover of Zeus, Io (mythology): Nominative Iō, Genitive Ious < *Iŏ-os. Io, transformed into a cow, is supposed to have crossed both the Bosphorus (“ox passage”) and the Ionian Sea, before being restored to human form.
Grammatically, I’m not convinced by Io; Sardŏnios ‘Sardonic, Sardinian’ is derived from Sard-ō, -ous “Sardinia”, but Sardō did also have a Sard-ŏnos genitive. So as Nikos says, it’s potentially something else. At any rate, it is unlikely to have anything to do with the Ionian tribe.