Linux – Any other distro offer like Ubuntu Software Centre

There is a version of Software Center in Debian 7: https://packages.debian.org/wheezy/software-center However, it does not offer commercial software.

That package is not available in Debian Testing or Sid. Interestingly, the Gnome package "Software", which is the same kind of gui affair is marked as being "not in Debian" for Gnome 3.12.

Ansible is an open-source software provisioning, configuration management, and application-deployment tool. It runs on many Unix-like systems, and can configure both Unix-like systems as well as Microsoft Windows. It includes its own declarative language to describe system configuration

(From Wikipedia.) Homepage (Github).

There are several others in the same category. Reading about ansible should give you vocabulary to search for the others, and compare, if needed. Nix is a newer contender. Some say "more complex, but maybe just right.". chef is also on the scene.

Ansible example for hostname myhost, module apt (replace with yum or whatever):

ansible -K -i myhost, -m apt -a "name=tcpdump,tmux state=present" --become myhost

The list "tcpdump,tmux" can be extended with commas. (The fact, that the hostname myhost is twice in the command-line, because we are not using a fixed host inventory list, but an ad-hoc one, with the trailing comma.)

This only scratches the surface, Ansible has an extensive module collection.