The very first Legend of Zelda was itself a Zelda legend, hence its title. It was also one of the first to be adapted to the contemporary Link-Zelda structure of the myths. The introduction of Link into this myth was shoddy and introduced a number of inconsistencies.
For example, it's said that Link is a wanderer from afar who rescues Impa from Moblins but when he arrives in Hyrule, he has to take the place of the unarmed and inexperienced Princess Zelda. And so this allegedly experienced warrior who just killed a bunch of Moblins arrives in Hyrule without so much as a sword in hand.
Similarly, the original myth featured Zelda assembling the Triforce of Wisdom, the only force that could stand against the Triforce of Power in Ganon's possession. Because it was the first to be adapted, there were concerns about disempowering Zelda by replacing her entirely with Link. As a result, a strange compromise was struck; One in which Zelda, after assembling the Triforce, then immediately broke it back down into its component pieces and re-hid them for Link to find.
By contrast, The Adventure of Link, true to its name, is the first Link legend. The importing of Zelda into it as the sleeping princess that Link awakens from her long slumber proved to be just as clunky as the importing of Link into The Legend of Zelda. Most notably, the confusing questions raised as to whether Zelda is meant to be the princess Link rescued in his previous adventure or the one he is rescuing in this new one.
Similarly, Zelda's nemesis Ganon is roped into Adventure of Link very awkwardly. Link's nemesis is his own dark shadow, with only a scant few mentions of the idea that Link's defeat will somehow result in Ganon returning... just because.
But the largest and most consequential of adaptations made to The Adventure of Link is the revising of the magic scepter Link uses to awaken the Sleeping Princess into the Triforce of Courage, a modern invention meant to tie Link more closely to Zelda and Ganon's mythos.
And this is where the study of the legends' history becomes rocky, as many scholars consider the very notion that the Triforce of Courage did not exist in the original tales to be downright apocryphal.