@Degernase that is pretty common in Manga and Other form of Arts like Paintings and whatnot...
BTW,
In Japanese it's called Star system
Earliest manga author who uses star system is Osamu Tezuka Star System. See Wikipedia for details of his star system.
Japanese version of wikipedia has a page for Star system of manga/anime
Manga/anime section describe 3 categories.
Clearly defined same name character. Osamu Tezuka, Fujiko Fujio, Shotaro Ishinomori, etc.
Different character, Different world. rave-master and fairy-tail are categorized to this. Other example is heal team in Time Bokan. This contains Team rocket in pokemon.
Same character, Same world. Negima, UQ Holder and CLAMP's manga are categorized to this. Each story is happen in same world, but focus to different time or character.
Outside of this, there are spin off story. Magical Project S from Tenchi Muyo, Magical Girl Lyrical Nanoha from Triangle Heart and Fate/kaleid liner Prisma Illya from Fate/stay night.
That Wikipedia page also mentioned about game. For example, In addition to 2d action, Mario is protagonist of cart game, tennis game and other.
~Credited~
Links
https://en.wikipedia.org/wiki/Osamu_Tezuka%27s_Star_System
https://anime.stackexchange.com/questions/8181/is-it-common-for-mangaka-to-maintain-the-same-characters-design-between-differen/13671#13671