Anime-tized mangas! How does that work?

Anime is a short term for animation.
Anime refers specifically to animations created in Japan, or created by Japanese artists.

Anime is not manga, nor the other way around.

Manga refers to printed comics, or cartoons in Japan. (In Korean pronunciation, it's called 'manhwa', but I guess 'manga' is more recognized internationally)

In Japan, most mangas are published in serials of manga magazines. That's how they get to be known to public at first. There are several kinds of manga magazines, and among them, the most popular magazine is Weekly Shonen Jumps, which has been circulating since July 2, 1968. 

Rather than monthly magazines, weekly periodicals are more selling. For example,

1. Weekly Shonen Magazine
2. Weekly Shonen Sunday
3. Weekly Shonen Champion
4. Shonen GanGan

etc.. These magazines have had more than 4 million to 6 million circulations per year, during their heydays

Shonen Jump has covered a large number of famous mangas. There are currently twenty-one mangas serialized in the magazine. 

The list of those mangas includes:(in alphabetical orders)

Bakuman, Beelzebub, Bleach, Gintama, HunterxHunter, Katekyo Hitman Reborn!, Naruto, One Piece, Nurarihyon no mago, ... ...

Some of the all time favorites were from here as well:(what I meant by 'all time favorites' can be different in every country)

Dragon Ball, Dr.Slump, City Hunter, Slam Dunk, Yu Yu Bakusho.... after then, Rurouni Kenshin, Yu-Gi-Oh

Okay, now let's get back to Anime, again.

Many popular mangas are made into animes. From those magazines' popularity survey, TV producers and editors prudently pick one. After having agreements with the original manga creator, they start producing.

Here's one example of anime-tized manga: Rurouni Kenshin

The original manga version of Rurouni Kenshin

  

'Anime' Rurouni Kenshin 

The key difference of Anime version from printed manga is usually early ending

Anime is mostly created after the manga has been made successful. So that makes story progress gap between anime, and that of its manga version. This could eventually change the whole story line(and the ending)of anime, which in turn makes conflicts between anime producers and manga artists sometimes.

Anime's story line usually goes faster than manga, and that's why it could end earlier than its original manga version.

To avoid that, 'original' episodes inserted into the story of TV anime version. They are created so that TV people will once again earn some time to have TV art works done before they get to catch up with the manga's story.

However, these TV 'original' episodes are not favored by the fans of original manga, since they are hurriedly made up, and often do not fit into its plot well.

Anime-tization can seem to be a very good deal for the manga creators. Nonetheless, as they say, if the anime isn't successful, people blame it on manga's quality, whereas if manga gains popularity, people think it's because of the anime.