The portuguese word vermelho and the English vermillion have the same origin. They have its origins in the latin word vermillus which means small worm and refers to the Cochineal that is an insect from which it was extracted the red color in the past.
The Latin for red is rufus which gave origin to French rouge and Spanish rojo.
Latin rufus is related to the germanic tree (cousin-like). A prior germanic word gave origin to German rot, Dutch rood and English red.
Well, the Romance language group and the Germanic language group are both Indo-European languages.
Only now I understood that the Russian word "червонный" (obsolete for "red"/"scarlet") really has something to do with worms (as it sounds): https://en.wiktionary.org/wiki/%D1%87%D0%B5%D1%80%D0%B2%D0%BE%D0%BD%D0%BD%D1%8B%D0%B9