The pyramids were different because the pyramids were "originally thought to be the final resting places of the pharaohs but more recent archaeological finds have uncovered that they were built with very narrow shafts extending from the inside to the outer surface for the purpose of lifting the pharaoh’s soul unto the heavens." And the ziggurats were said to have been built for the gods. Or as a dwelling for them.
So, ziggurats were built in ancient Mesopotamia while the pyramids were built in Ancient Egypt. and
Architecture is different in both structures.