In which cases should I use the ZIP package instead of the installer?

The majority of users will be happy to use the exe installer. We recommend to do so, it is the easiest way to get started.
However, there a some use cases in which you might prefer the ZIP version:

Using Greenshot without installing, e.g. if you want to use it portable.
As Greenshot can be started without installing it, you can use Greenshot for instance from a USB stick. Just extract the .zip to a directory and start the Greenshot.exe from there!
The settings and log will be stored in the same directory, this really makes it portable.
Installing Greenshot with your own or third party installer, for instance when you want to deploy Greenshot to multiple PC's.
Package all the files, make sure to include the license, except the plugins and languages you don't want and copy then on the target PC. You can supply your own settings, as is described in the setting.