Or Chocolatey: http://chocolatey.org/packages/paint.net/
cinst paint.net
This is how you should install software on any OS. If you're still hunting for downloading links you're doing it wrong.
Chocolatey is great, but unfortunately package managers don't work for every piece of software on every OS. Period.
I think package managers becomes less useful to average users when you can't expect all of your software to be there.
Other than that they're literally identical to something like synaptic.
The biggest difference I see is that package managers on most Linux distributions are designed to be extensible to support other sources. Application stores generally are not.