Hi Jonathan,
My name is Igor, it's a pleasure for me to help others and I'll do all my best to help you.
When a screen is turned off, a PC works as usual, just show you nothing. During sleep some computer components are powered but other don't, and computer cannot do any work on background.
You may lock your laptop (Win+L); your session and all apps will run as usual, but screen will show welcome screen and it will be needed to enter Windows to continue working and see the screen.