Here's a breakdown:
* Anime: The 2006 anime adaptation of D.Gray-man ended at episode 103, covering the story up to the 68th chapter of the manga.
* Manga: The manga continues after the anime's ending and has over 200 chapters as of 2023.
* Anime: There is a sequel anime series called "D.Gray-man Hallow" which started airing in 2016, continuing the story from where the first anime left off.
So, while you can watch the first anime series until episode 103, it's just a portion of the full story. To experience the entire D.Gray-man saga, you'll need to continue with the manga or watch the Hallow series.