The Wiki is a good place to find specific instructions for the Pinephone and get going from there. The linked section explains how to flash an OS to the internal storage of the phone, so that is how you would replace your current installation. If you want to keep your current installation, you can also flash an OS to an SD card. For that you can just use Etcher as described in the thread you linked. No need to do anything beyond flashing it to the SD card and inserting that into your phone. Your phone will boot automatically to the OS on the card if there is one. (Edit: Link to the Wiki article with all the installation instructions. I believe the resizing part is done automatically by most distributions by now, but I'm not sure about that.)
Manjaro is indeed a general Linux distribution, but they, as all the other distros available for the Pinephone, have a dedicated ARM version (packaged with one of the 'desktop' environments for phones like Phosh) to make it work on devices like the pinephone which have a different processor architecture than most desktop PCs. So you cannot install the desktop version on your phone, but have to use the ARM image. The current Phosh image for Manjaro can be found here. An earlier version of that image (Beta 1) is exactly the one that had been installed to your Pinephone at the factory, so you won't lose anything compared to when you got your phone. You might want to back up your home directory though and possibly some stuff in /etc (like WiFi configuration) before flashing a new OS to keep your personal configuration and data. You can just transfer that stuff to the according directories in the new OS installation.
Manjaro is indeed a general Linux distribution, but they, as all the other distros available for the Pinephone, have a dedicated ARM version (packaged with one of the 'desktop' environments for phones like Phosh) to make it work on devices like the pinephone which have a different processor architecture than most desktop PCs. So you cannot install the desktop version on your phone, but have to use the ARM image. The current Phosh image for Manjaro can be found here. An earlier version of that image (Beta 1) is exactly the one that had been installed to your Pinephone at the factory, so you won't lose anything compared to when you got your phone. You might want to back up your home directory though and possibly some stuff in /etc (like WiFi configuration) before flashing a new OS to keep your personal configuration and data. You can just transfer that stuff to the according directories in the new OS installation.