A lot of anime that we watch, mostly originated from Mangas. Examples include the classic Doraemon. Those that don't originate from Mangas, may come from other story sources, such as games (Fate Stay Night), light novels (Bakemonogatari), or purely original (Gundam Seed.)
Anyway, what I am going to talk about, is how some of these adaptations, particularly those from Manga, differ from their anime counterparts. A lot of times, when an anime is created, the contents inside are inconsistent with the original story, sometimes to great extents. In a way, you could say that they are not canon - not true to the original storyline.
Obviously, it is a great honor for an author, to have his/her work adapted to an anime. But I can't understand why these authors would agree to have their works altered in such a way, until it doesn't even resemble what they first did? Personally, if I am an author of a story, I wouldn't change the contents inside, due to someone's request, simply because he dislikes it. More often that not, some of these changes were greatly unnecessary, and leaving it as it was, would have done better justice than changing the original work. In short, not always logical or reasonable. It is hard for me to fathom why these authors would agree to these changes.
Anyway, here, I will list down some of the animes that I have watched, and how much they differ from the original work. You decide if these changes were necessary. If you think you can add to the list, please do so.
Skip BeatI followed the manga and anime quite closely. One of the biggest difference is how they completely removed Kanae's story arc. The entire section, worth nearly 3/4 of one volume, was omitted.
Other significant changes, include changing that Mimori did not know Kyouko. Also, the part where Saionji's cronies trying to sabotage Kanae, was greatly shortened, which was a shame, since that is one of the funniest parts in the earlier chapters. Although not specifically clear in the final chapter, apparently, they removed the part where Kyouko shows up as Bo in a duck suit as well. Other minor changes include Kyouko getting lost after her conversation with Ren as Bo, or changing her middle finger into a thumbs down. (It's actually understandable in a way.)
Some of these changes, are particularly redundant, especially the Mimori part. As I watched the anime, I personally found some of the metaphorical parts needlessly exaggerated, to the point where it was somewhat annoying. In the Manga, these metaphorical parts (such as the part where Kyouko imagines Ren and Shou on their knees), where drawn in one picture with only a few lines, and it wasn't "in-your-face". I personally did not like the anime's annoying exaggerations.
Loki Matantei RagnarokI watched the anime complete, and only a few chapters of the manga. But I can say this much, it will be a much easier effort to list out the similarities, then find the differences. If I were the author, I would be like, "WTF? Is this my story?"
The anime seems to grossly focus on the comedy etc. The manga, I can say it is darker, and more bloody. If they wanted comedy, this shouldn't have been the top choice for adaptation.
Zoids Chaotic Century / Guardian ForceI watched the entire series, and read only the first book. In Japan, they are simply known as Zoids Anime, part 1 and 2.
Again, apart from using the same characters and settings, NOTHING is similar between the anime and manga.
I dare say that for this, I loved the anime many times more than the Manga. I didn't like the Manga at all, but I really love the anime series.
Samurai Deeper KyoAgain, as I would call it, another WTF series. There's really very little similarities between the Anime and Manga. I watched the entire anime, and only a few chapters from the manga, and I was like, "What the hell?"
In the manga, there were none of these Kenyos, and there's Botenmaru.
In the anime, there's no such person as Botenmaru, and the storyline extends way, way further than the anime. Last episode was as confusing as hell, I recall.
To be perfectly honest, I prefer the drawn anime version of Kyo. The manga version of Kyo, the way he grins, looks like a naughty boy or pervert smile to me. The anime version, that bloodthirsty, diabolical smile looks more real, has more impact.
Love HinaI read the whole manga for these series, and watched only a few episodes. In the Manga, there was no rich handsome guy chasing after Naru, and there were no freaky old men. I don't know why the hell they threw these inside the anime.
To be honest, the manga is very funny, but the anime is agonizing to watch. The only humor within the anime itself, seems to centralize everything on having Keitaro getting the crap beaten out of. The comedy that was in the Manga, is really lost. One of the reasons why I don't feel like reading or watching Negima.
TrigunOnly read a few chapters, but watched the whole anime. Much of the whole story remains intact. I noticed the anime did not follow the same order as the events in the Manga, though. For parts of the story in the manga, where the 2 girls didn't appear, they were included in the anime version of those parts.
MonsterA series that I hated. I compared the endings and beginnings of the anime and manga. They all matched. Possibly one of the rare true-to-manga anime series. Even the unique (but less-than-pretty) art style was kept.
Shining Tears X WindAnime adapted from the game Shining Wind, it focusses on Souma's storyline, rather than Kiriya's. I watched anime and completed the game.
Overall plot remains the same as the PS2 game, but there are still some very significant changes. In the game, Souma is to be executed by burning, but he is saved by Zero. Later, Shumari tries to escape, but he is stopped and killed by Killrain. In the anime, a cannon blast from Baelgard's ship killed Shumari, but Souma is saved by Zero. All shortened to one single event. In the game, Souma was not present in a few events, but the anime threw him and his party inside some of them. Examples include Lassi finding the secret entrance, Souma and group was added in that scene in the Anime. Several events were also shortened. In the game, there were a few series of events or battles before something happened, but the anime cut most of the unimportant ones out. In the scene where Kiriya and Xecty fell in the crevasse, in the game, he pulled out her Shinken. This did not happen in the anime.
The game never mentioned Traihart's name as Saionji, it was in the anime only. The anime also never showed Kiriya pulling anyone's normal Shinken except for Shiina and Kureha.
Neo Angelique AbyssI played the game and watched both seasons of the anime. In the game, when Ereboros awakens, the game is already near the end. In the anime, it's only the end of season 1. Season 2, you could say follows an almost entirely original storyline. New characters were added in the anime, such as Roche, Mathias, and Jet. Mathias did not exist in the game, and Rene was already the leader.
Personally, although I don't dislike the game, I think I prefer the anime storyline.
Full Metal Alchemist2 anime series have been released for this manga. Rather than a continuation, the second series is a different version of the same story.
I watched the whole of the 1st series and movie for it. From the reports, the anime series differ from the manga halfway through, following a different plot. This is supposedly due to the request from the author herself.
(The movie for the anime, in a way, wasn't consistent with actual historical events. :P )
Second series, Full Metal Alchemist Brotherhood, is supposed to follow the manga closer. But I watched the first episode, and it wasn't about Lior. This is supposed to be closer to the manga? 0_o
Anyway, although I haven't watched much of the 2nd series, I have to say I like the 1st series very much. It is still one of my most favorites.
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Right now, these are all the series I can think of at the top of my head. If you have any you can add to this list, or have something to say, please do.
Anyway, I'm trying to highlight that most anime series do not follow the manga storyline very closely. Sometimes, it's understandable, but more often than not, the change is unnecessary. Personally, as a fan, I do not like adaptations that do not follow the original storyline well. (Be they manga-to-anime, or anime-to-manga adaptations.) Sometimes, the creators of that anime or manga adaptation of the originals, they make changes that they see fit, without considering whether fans or viewers appreciate these changes.
Personally, from my own standpoint, if I were to create a story, and someone else takes it and change it in any way he likes, I would consider that disrespectful. I do not know why authors of these works would agree to have their work altered in such ways. I'm pretty sure fans of these respective series, don't particularly approve of these changes either.
I read the first 2 books of Harry Potter. I watched the 2 movies, and from what I know, most of the plot remains intact. If I recall right, some unimportant events were removed, but most of the plot remain true to the book. I believe that's the way it should be done.