In the manga, Guts' character development is explored more deeply. The anime might focus more on visual action scenes. Also, the art style can vary, with the manga having a certain grittiness that the anime might not fully replicate.
The 'Guts' anime is a fairly close adaptation of the manga. It keeps the key elements intact, like character development and major plot points. However, there might be some added background details or minor character expansions to flesh out the story in the anime.
Guts is purely fictional. It's a concept or character that exists within the realm of imagination and creative storytelling rather than being based on reality.
Perhaps in this fanfic, Griffith has turned into something truly evil and a threat to the world Guts cares about. Guts, being the warrior he is, might feel it's his duty to put an end to Griffith to save others. Also, Guts could be driven by his own sense of justice. If Griffith has wronged innocent people, Guts may decide that killing him is the only way to set things right.