There are two different software apps in Ubuntu 20.04, Software
and Snap Store
. The Snap Store and the Software app can be installed alongside each other without removing either app. If Ubuntu Software got removed in 20.04 it can be reinstalled by running sudo apt install gnome-software
. If the snap-store is not currently installed it can be installed if by running sudo snap install snap-store
.
Ubuntu Software icon in Ubuntu 22.04: 
GNOME Software icon in Ubuntu 22.04: 
All the apps in the Snap Store are snap packages. If you're searching for a snap package it's more convenient to search for it in the Snap Store, because sometimes the same app has two packages in Ubuntu Software, an apt package and a snap package, but the same app has only one snap package in the Snap Store. If you're searching for an apt package and don't want to use the terminal you may want to install the old Ubuntu Software app with sudo apt install gnome-software
. When you install the gnome-software package in Ubuntu 20.04 it is named Software, and the app that was named Ubuntu Software in the default installation is renamed as Snap Store. In Ubuntu 22.04 and later the Software app's name has been changed back to Ubuntu Software and clicking the orange shopping bag Ubuntu Software icon launches the Snap Store instead.
The Snap Store itself is a snap package, so it can be installed in any Linux distribution that supports snap packages without causing package management issues. snapd has been ported to a wide range of Linux distributions to enable snaps to be used across any Linux distribution, including Debian, Kali Linux, Raspbian, Fedora, CentOS, Arch Linux, Manjaro Linux, and openSUSE.

Snap Store
sudo apt install gnome-software
. – karel Jun 20 '20 at 09:53@karel I wouldn't say it is so widely supported. https://www.zdnet.com/article/linux-mint-dumps-ubuntu-snap/
– pktiuk Jun 20 '20 at 14:09sudo apt install ubuntu-software
. This command installed gnome-software and the snap plugin. – Steve M Jun 20 '20 at 20:59ubuntu-software
package has been converted to a transitional package. – Gunnar Hjalmarsson Jun 20 '20 at 22:57snap-store
in the terminal launch Ubuntu Software, Orange bag like icon.. but it is really Snap Store in the hood, the true snap store package, not an alt. Installing and runninggnome-software
run the "true" old software manager where you can choose between snap package and deb packages... and its icon is blue. Well done Canonical... – B. du Garay Jun 21 '20 at 23:34$ sudo apt install gnome-software Reading state information... Done Package gnome-software is not available, but is referred to by another package. This may mean that the package is missing, has been obsoleted, or is only available from another source E: Package 'gnome-software' has no installation candidate
This used to work, but apparently not now. Ubuntu 20.04 – zipzit Mar 21 '21 at 10:54