Content differences: Computer science focuses on foundations of computing including, algorithms, programming languages, theories of computing, artificial intelligence, , and hardware design. Software engineering, on the other hand, focuses on technical and managerial leadership for large and complex systems. Its foundation of enduring engineering principles will support a lifetime of practice amid emerging technologies.
On the delivery side: Computer science programs tend to concentrate on individual assignments, dealing with the development of systems such as databases, compilers, and operating systems.
But software engineering is anchored in real-world problems. Because software engineers apply professional judgment acquired through practical experience, their training is hands-on, project focused and team-centered.
Computer science: study of the computational methods, math and algorithms. It's a subfield of mathematics: Discrete Mathematics. Scope: from 1 + 1 = 10 (including Big O Notation) to P is / not is equal to NP. Work: from correcting students papers in an oscure university or a junior software developer in a small start-up to being a senior lecturer in Caltech or a senior lead developer in Google or Netflix.
Computer Engineering: how to make hardware that computes or peripherials for computers. Scope: from the microprocessor (including computer networking) to the mouse or touchscreen. Work: from soldering an integrated circuit of calculators for a parts developer start-up to managing the operations of Intel or Apple.
Software Engineering: how to make software that serves a purpose and makes the hardware to behave properly, alone or within the scope of a team. Scope: from an operating system (including programming languages), to facebook or Quora. Work: from coding a "Hello World" (including a system that prints invoices) to managing the operations of Facebook or Google.