The 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.
Computer engineering deals with computer systems and understanding the most practical approach to computer development and use. Although, computer engineers focus on the software, a computer engineer is also required to be familiar with the hardware. Additionaly, Computer engineering combines electrical engineering and science, with a focus on software-hardware interactions. Some of the most common programs offered in computer engineering include processor interfacing, digital logical design, thermodynamics, power management, solid state physics, and magnetic fields. Degrees in computer engineering are highly customizable, as programs often cover a wide range of interests. Ultimately you are in control of your own degree as you focus on your interests, this customizable degree will propel your profession into your desired career direction.