For example, I ssh into a server and run a command say ... wget, then I close the terminial window. Do my download continue? Or does it depend on the app? If so how do I know?
It depends.
If you're closing a SSH session, you're logged out and all active programs are killed. This might become problematic if you've frequent connection drops and therefore it's recommended to use the screen program in a SSH session if you do not want to loose your session on exit.
Most programs are gone after a closed SSH connection if they're run on the command line, e.g. nano or apt-get. do-release-upgrade also uses screen and won't be interrupted by a connection drop.
