Great question — answering as the UphillTech team:
I know this question is 5 months old, but someone just asked me the same thing in IRC! AFAIK, there hasn't been a software center-type app in Debian for years...since Debian 5 or maybe even before that, I believe. But take heart, all is not lost. I'll briefly explain. I used Ubuntu for a while, and for me the Software Center was just "okay." I currently use Debian Buster (upgraded from 9.2 Stretch) with Kernel 4.13.4-2 (2017-10-15) just so you know. You don't need a "software center." Just use open a terminal and type apt show "packagename" without the quotes. You'll get info about it if the package is available for you. If you must use a GUI, then use Synaptic. In my Cinnamon DE it's under...
Full answer by mem: https://superuser.stackexchange.com/a/1266175 (CC BY-SA 3.0).
Need it done for your business? UphillTech.