Gnome-Software stor vs Synpatic

Gnome Software has plugins (which Zorin OS includes by default) to include sources that allow managing different types of packaging formats, i.e.: flatpak and snap.
Synaptic only works with Zorin OS's native package format: deb.

This has both advantages and disadvantages. One the hand one there are more options available, but on the other hand it's more confusing to people who are not aware of the, admittedly complex, package format available in Linux. For example here you can see that the same software has 4 different available options:

Sometimes there are differences in how these programs are labeled in one store and there are duplicate entries:

If you are interested you can read about the difference between packaging formats here.

Another difference between Gnome Software and Synpactic, as pointed out by Aravisian, is there's better feedback as to what will be installed or uninstalled. Most programs have dependencies: other programs that it needs to run properly. In general you shouldn't need to think much about it, if at all, but it can be useful to understand what's going on and it helps with troubleshooting later.