Ah those files.
They can show info when user is logged in, or not logged in.
welcome_logged_in.htm
Currently that shows the "Welcome username and menu" at the very top when a user is logged in. So only stuff for logged in users, in this case a navigation.
welcome_not_logged_in.html shows the login form you see at the top ( the small button at top "Login" ). So this file can be used to display stuff for only visitors, in this case a login form
And {$wrapper_welcome} is a template tag, which is responsible for showing that info, which is in those 2 files