Solution 1:

The two aren't really inconsistent - the sudo command always changes user, either to root, or to the user you specify with the -u switch. All the -s does is provide a shortcut for starting a shell as that user. It is really equivalent to:

sudo $SHELL

except that it will likely fallback to /bin/sh or something if SHELL is not set.

Solution 2:

sudo -s runs the shell specified in your $SHELL environment variable as the superuser/root. You can specify another user using -u.

The $SHELL environment variable contains the path to the user's default login shell. The actual setting for the default shell program is usually in etc/passwd. Depending on what you've done in your current session, the $SHELL variable may not contain the shell program you're currently using. If you login automatically with zsh for instance, but then invoke bash, $SHELL won't change from /bin/zsh.

Show the current user and shell program:

echo $(whoami) is logged in and shell is $0
  • whoami prints out the username the user is working under.
  • $0 contains the name/path of the currently running program (shell program in this case).

Solution 3:

From the manual:

sudo allows a permitted user to execute a command as the superuser or another user, as specified in the sudoers file.

-s Shell, runs the shell specified by the SHELL environment variable if it is set or the shell as specified in passwd(5).

More seriously, the sudo -s run a shell environment variable. Since you didn't add any variable it run as specified in passwd, and so connect you as root.

Solution 4:

Have a look at this post from superuser:

What's the difference between the commands "su -s" and "sudo -s"?

By the way, your post should be moved to superuser (or askubuntu as said in comments)!