Applications Not Closing Fully (MAC)

The red button is meant just to close the active window, not the app itself. Some apps may completely close out when you click the red button on the last open window, but many apps will remain open.

If you want to quickly close an app, just use Command + Q, or use <App-Name-menu> --> Quit. For example, click on Chrome on the menu bar and select "Quit".

To keep apps from re-opening automatically when booting or logging into your user account make sure those apps are not listed in your user account's Login Items.

Remove login items to resolve startup problems on your Mac - Apple Support

Also, when you log out, reboot, or shutdown.....make sure to "Reopen windows when logging in" is unchecked on the pop-up prompt you get to confirm logout/restart/shutdown.

Prevent apps and windows from reopening on Mac - Apple Support

Just to add two previous good advise from @HWTech

Application like Safari, Mail and Notes ( there are more ) will close the windows and still remain loaded

You can tell this by looking on the Dock

Example is Safari is open and I am using it. But, the Black Dot beneath Mail and Notes indicate the application are Not on Screen and are still loaded

Other Applications like Photos, Contacts and some other. When you click the Red Button, they close completely

User wrote " Also, is there a way to stop applications like Google Chrome and Spotify from opening in the background automatically when I start up my computer? "

Check in >> System Setting >> Login Items

Are the two application listed in your computer to start when the computer starts ?