Digimon
Digimon Story: Cyber Sleuth is the first game in the Digimon Story subseries to have been released outside of Japan under its original title. The first three games were released as part of the Digimon World series in the West and the three in between never got a Western release.
Contributed by Mass Distraction
On November 19th 2015 Digimon v-pet designer Oota Kensuke, also known as "Volcano Oota", revealed in a youtube video that the Digital Monster v-pet was originally called Otokotchi, from the Japanese word Otoko "boy" and the existing franchise Tamagotchi (Tamago "Egg" + Uotchi "Watch").
It was ultimately changed to Digital Monster because the team thought it sounded "cool".
Contributed by saifors
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The entire Digimon franchise started out as Digimon V-Pet, a sort of a spinoff of Tamagotchi. The very first v-pet, called Digital Monster Ver. 1, featured a few differences from most other iterations of the franchise. Notable differences include Agumon having 4 fingers instead of 3 in the artwork, Devimon being named Darkmon and Monzaemon being named Teddymon.
Contributed by Mass Distraction
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Digimon Digital Card Battle had different card backs between the american and japanese versions of Digimon Digital Card Battle, which also applied to the physical card game at the time.

The card backs were unchanged in the english dub of Digimon Tamers, which is also true for Digimon World 3 (in spite of the card game in Digimon World 3 not actually being the same one).

Oddly the english version of Digimon Rumble Arena, which was mostly based on Digimon Tamers, had the american card game backs in the american version instead.
Contributed by mattwo
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There are a few differences in the western localization of the entire Digimon franchise, aside from some of the names being different, the words "Digivolve" and "Digivolution" replace the words "shinka" and the translated version of "shinka", "evolution" both verbally and visually.
Contributed by mattwo