What are package formats?
A package is a file that describes how and where software is installed in your OS. Manjaro is not responsible for the contents or quality of the installed software, only install software if you trust it.
Native packages, as the name suggests, are packages that are specifically built for Manjaro. They are officially supported and usually depend on other packages in the system to function properly.
Portable 3rd-party-packages work across distributions unlike traditional native packages.
Flatpaks are self-contained packages with inbuilt dependencies and do not depend on the system to run.
Snaps are self-contained containers that could have dependencies. It's more or less the same as running Ubuntu with a Manjaro Kernel.
Appimages are portable single file package that runs on usespace without the need for being installed.