I never played OOT growing up, but I did watch friends play it and ever since have had the "Lost Woods" song stuck in my head, which I recently learned on ukulele. Specifically, this version. However, I've become aware that it is similar/identical in melody to Saria's Song. Here is an example compilation. When people cover the song, they will frequently refer to it by both titles. (can't link example but just search lost woods cover on youtube.) What is the difference between what each title refers to, if there is any? Knowing what the actual title is to look up on chord/tab search engines is really helpful towards finding good arrangements.
The difference as a composition is nearly zero.
In the game, the Soundtrack "Lost Woods" plays as a background music when you walk through the eponymous Lost Woods, while "Saria's Song" is a music piece Link learns during the game for his ocarina. When you play Saria's Song, you are able to talk to Saria, a friend of Link who lives like him in the Kokiri forest. There isn't a real statement from Nintendo, but I guess that they used the Lost Woods Soundtrack as Sarias Song to show the connection between Saria, the forest and Link.