gksu would normally log in the root user and run an app on this session
IN some systems like ubuntu, gksu and gksudo are symlinked which basically means no matter which command used you are simply using gksudo because /apps/gksu/sudo-mode is enabled
Normally gksu would log in the root user and run an app on this session. Where as gksudo/sudo keeps the user logged in and elevates the root-level privileges to that user
You should never use normal sudo to start graphical applications. You should use gksudo instead. gksudo sets HOME=~root, and copies .Xauthority to a tmp directory. This prevents files in your home directory becoming owned by root. (AFAICT, this is all that's special about the environment of the started process with gksudo vs. sudo).