In GUI tesing we do the usability testing and appearence of 
the web pages but in the black box testing we do the 
functionality tesing this is the basic diffrence between 
this two

GUI Testing is a part of Black Box Testing. Its one kind of 
Black Box Testing Technique

GUI testing is part of black box technique.
   In black box technique we have 3 types of testing.
1.usability testing
2.functional testing
3.performance testing.
     GUi testing comes under functional testing.
  In gui testing we will check  whether the properties of 
the object function accordingly or not.we will check the 
focus,enable ,disable properties of the objects.

for example when the yahoo page is open the control goes 
default to username,and after entering the username and pwd 
Ok button shud be enabled.

gui testing comes under black box testing, where we r going
to check whether the alignments of the objects r placed
properly or not.. like look and feel we can also say that
this isw cosmetic testing

black box testing is testing the overall functionality of a
system without any impact on the internal code of an
application. here u r going to perform the usability, gui,
functionality, validation, security, system, performance and
user acceptance testing.

regards
SM