Content editor web part is a place holder for creating rich text on on the page. This gives a cumbersome output with mixture of HTML and scripts inline. Now you don’t need to bother about mixing the content with scripts. This can be easily separated with Script Editor web part.
Coming to differences both renders in same way on page including div structure and internal elements. The only difference found between these web parts are Content Editor web part can be exported and script editor web part doesn’t allow you by default. Script Editor web part having default export mode of ‘Do Not Allow’.