Fcitx5-mozc is Mozc engine for fcitx5. 
Mozc is a Japanese Input Method Editor (IME) designed for multi-platform

What's Mozc?
For historical reasons, the project name Mozc has two different meanings

Internal code name of Google Japanese Input that is still commonly used
inside Google.
Project name to release a subset of Google Japanese Input in the form of
 source code under OSS license without any warranty nor user support.
In this repository, Mozc means the second definition unless otherwise 
noted.

Detailed differences between Google Japanese Input and Mozc are 
described in About Branding.
( https://github.com/fcitx/mozc/blob/fcitx/docs/about_branding.md )
