Ubuntu is a Linux-based operating system built on Debian's architecture and infrastructure. Ubuntu is probably the most popular Linux-based desktop operating system.
Manjaro is a Linux distribution based on Arch Linux. It has a focus on user friendliness and the system itself work fully "out of the box".
The purpose of Linux Mint is to provide a desktop operating system that home users and companies can use at no cost and which is as efficient, easy to use, and elegant as possible.