Not exactly. In 2011, the producers of Zelda finally created an official timeline of the series, which details how all installments are related to each other chronologically. They had to account for many continuity problems and discrepancies that had arisen over the decades, so their chronology splits in 3 separate timelines in Zeruda no densetsu: Toki no okarina (Ocarina of Time). The first timeline continues the child era from Ocarina of Time, and gives rise to Zeruda no densetsu: Mujura no kamen (Majora's Mask) and Zeruda no densetsu Towairaito purinsesu (Twilight Princess). The second timeline continues the Adult era, where the Seven Sages are Link's friends of different species, who help him seal Ganon into the Sacred Realm. This timeline leads into Zeruda no densetsu: Kaze no takuto (Wind Waker), Zeruda no densetsu: Mugen no sunadokei (Phantom Hourglass) and Zeruda no densetsu: Daichi no kiseki (Spirit Tracks).The third timeline in Ocarina of Time is unseen, and occurs when Ganon is successful by defeating Link. By obtaining the Triforce pieces of both Zelda and Link, Zelda and the other sages can only send Ganon away into the Sacred Realm. When Ganon attampts to escape years later, the King of Hyrule appoints Seven Sages, who re-seal the entrance to the Sacred Realm, again trapping Ganon inside. Generations later, Ganon manages to make the descendants of the Sages disappear, weakening the seal and allowing his escape.Link to the Past is a successor to this specific backstory: the Seven Sages are men and Link has to find their descendants (also human) to defeat Ganon. It is also interesting to note that the nature of the imprisonment is different in the timelines. In the first, Ganon is cast away in what is later identified as the Twilight Realm (seen in Twilight Princess); in the second and third, Ganon is imprisoned in the Dark World (the Sacred Realm turned dark as it reflects the dark nature of his heart), which is shown only in Link to the Past as a twisted version of Hyrule.
Everything that might come across as being religious was altered by Nintendo of America. Not even the subtitles stayed untouched. Parts of the story were changed for the same reason. One example: Agahnim is no longer a priest but a wizard. A detailed comparison between both versions with pictures can be found here.