he primary difference is that computer science was originally a sub-branch of mathematics. Computer science deals with the basic structure of a computer and is more theoretical. Hence, it is more malleable in terms of specialization, with the emphasis on math and science. Software engineering is a field concerned with the application of engineering processes to the creation, maintenance, and design of software for a variety of different purposes. A software engineer designs customized applications per the requirements of an organization.
For more info:  difference between software engineer and computer engineer
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