ano je v tom rozdil...
man sudo
-s [command]
The -s (shell) option runs the shell specified by the SHELL
environment variable if it is set or the shell as specified
in passwd(5). If a command is specified, it is passed to
the shell for execution. Otherwise, an interactive shell
is executed.
-i [command]
The -i (simulate initial login) option runs the shell
specified in the passwd(5) entry of the target user as a
login shell. This means that login-specific resource files
such as .profile or .login will be read by the shell. If a
command is specified, it is passed to the shell for
execution. Otherwise, an interactive shell is executed.
sudo attempts to change to that user's home directory
before running the shell. It also initializes the
environment, leaving DISPLAY and TERM unchanged, setting
HOME, SHELL, USER, LOGNAME, and PATH, as well as the
contents of /etc/environment on Linux and AIX systems. All
other environment variables are removed.