Aristotle was Plato's student. Therefore, it should not be surprising that there are many similarities concerning their philosophies. However, there are a number of notable differences as well. One major difference is that Plato was concerned with ideas and ideals and Aristotle was much more concerned with what is real and tangible. In many ways, Aristotle rejected Plato's idealistic notions and wanted to root ideas in what was readily observable. That is why Aristotle was much more focused on the sciences than Plato who focused on the realm of ideas.
Plato felt that concepts all had an ideal form and that there was a universal form to all notions. This is often referred to as the Platonic ideal, meaning that everything is rooted in an idea that encapsulates its true essence. To Plato, everything could be measured against that idea. Aristotle, for his part, believed that each instance of something had to be addressed individually and those universal ideals did not actually exist.
While both philosophers believed in the high power of thought, they differed on how thoughts are related to the senses. Plato said that the senses have the propensity to mislead one's thoughts. Conversely, Aristotle argues that our thoughts can only be truly informed by our senses.
In terms of government and politics, they differ once again. Plato expounded the notion of an ideal state. In this state, there would be no private property for people to fight over. Even family units would be supplanted in favor of a unified state and society. To Plato, the ideal state would remove the problem of human selfishness. Aristotle took a more realistic approach to politics. He knew that people would never actually surrender all their private property and interests for the public good. He did not believe that people would ever actually completely abandon their selfish ways. In fact, he saw human selfishness as a force for progress in many ways. Aristotle considered the state to be a force to create a balance between people's personal interests and the greater good.