most commonly referred to as the "happy ending", is where you save at the first poem game, and write a poem just for one girl throughout the week. you do this for every girl (sayori, natsuki, yuri, haha fuck you monika). the main goal is to see every characters special scenes (such as natsukis baking scene or yuris rag cheek escapade). both endings are canon to the game.
deleting monika or sayoris .chr file before you boot the game up will end at the "now everybody can be happy" scene with sayori hanging. not so much an ending, just an easter egg.
writing all the poems for each girl does result in different poems from each later on, but i cant remember what those poems are.