4G is a term for a category of mobile service (i.e. 4th Generation) whereas LTE is a standards based technology that is 4G compliant. Sprint/Clearwire use WiMax to implement their 4G wireless service. Of course, the ITU-R has stated WiMax nor LTE are "technically" 4G...only WiMax-2 and LTE-Advanced can be declared 4G. It's kind of how Dish, DirecTV and Cable (in most areas) sell their HD when it is in fact HD-Lite.
They didn't really change their definition, they simply gave up trying to enforce the real definition, and said "Call it whatever you want." The ITU-R stands by their original definition.