From Joaquim Varandas:
GUI Octave is a Graphical User Interface for the GNU Octave high-level language.
GNU Octave provides a command interface for solving linear and nonlinear problems numerically, and for performing other numerical experiments using a language that is mostly compatible with MATLAB. It may also be used as a batch-oriented language.
GUI Octave provides a convenient graphical user interface to simplify the use of GNU Octave for user who don't like the original command line based version of GNU Octave, but still want to use the GNU Octave potential.