There are two different Skype app, one that you download from Windows Store, and second that you download like a program and install. Although you can close the Skype from the Taskbar, It is not a convenient way every time.
Skype starts automatically and remains in the background when you Sign in to Windows 10. Windows 10 signs you automatically into Skype, So that you could available to receive calls and messages. As soon as you start your PC and sign in to Windows 10, Skype starts bothering you with a number of notifications.