User blog comment:7-45 Fire/YeahWinx (form) page has a flaw/@comment-2056915-20171127042358/@comment-29197449-20171127043654

Adding onto your point regarding "worlds" and "realms," the Winx are technically from different worlds; they're just all a part of the Magic Dimension. Domino, Solaria and Melody for example are all a part of the Magic Dimension in the same way as Earth, Jupiter and Neptune are all part of the Milky Way Galaxy.

Though, them being from different worlds doesn't really matter since, as the Winx Club, the original five came up with the term and seemed to use "Winx" as a name for their base forms. Aisha most likely used the name as well when she finally realized that she was the newest member come Season 2 but, as you already said, that's just us assuming things. As for the Alfea Fairies, it can also be assumed that their base forms are referred to as "Winx" after Faragonda made it an official term for the modern fairy by the S1 finale.