Final Fantasy Adventure is actually Seiken Densetsu in Japan, but it was given the Final Fantasy name in America for more name recognition. It is still part of the "Mana" series, as Seiken Densetsu 2 is what we know as Secret of Mana.

Secret of Evermore is not part of the Seiken Densetsu series, Seiken Densetsu 3, also for Super Nintendo, is what many of us know as Secret of Mana 2 and while a great game, was not released in America. There are several ROM translations of the game on the internet, but as this site does not link to ROMs and the like, I will not give you any further information on that.

I'm not quite sure where the later Mana games fall into the fold, as I believe both occured after the Square and Enix merger.