Hello Writer-Ben, thank you for checking out Wilderlands! This is a great question, and something on reflection that could be clearer in the rulebook, especially for non-native English speakers.
The primary mechanical difference between the two is that Songs are used in combat, and upon failing a Heart (HRT) save, make your character fatigued so they cannot use another song until after a brief rest like stamina. Sagas can be used at any time, and either give a passive bonus, or can make your character Deprived after use depending on the Saga . As far as the 'lore' goes, I left the details of what a Saga looks like up to the Chronicler to fit their vision of the game. In my own homebrew setting, Sagas are found as magical scrolls or tablets in dungeons, and Heroes absorb their power upon reading them and learning of the mighty deeds of old. However, a Saga could also be a physical book or scroll read from each time it is used, or a runestone that is channeled if you prefer.
Meanwhile, Songs are taught by wise lore masters or captains when good deeds are done for their people. I encourage players to narrate how their character sings or chants during battle, but of course this is optional! I encourage you to change the flavor or styling of both mechanics to match either your homebrew world, or align with Middle Earth directly should you choose to run a game in Tolkien's world. If you have any other questions please let me know.