Computer science is about extending the art and science of computer programming.
Software engineering is about applying engineering principles to computer programming. Engineers in general not only have to know what the technical ins and outs of what they are doing, they also have to know how much it will cost, how long it will take, where the risks lie, what problems are just lurking about waiting to bite them.
The budget for even a small software project can easily exceed a million dollars. Grand Theft Auto 4: $100 million. Suppose you have just five to ten software professionals working on a project for just a year. Add their salaries, plus benefits, plus office space, plus computer equipment and software, plus G&A, plus the tiniest of profit margins and you have a million dollars, more or less. Winging once was an option with regard to software development. Not any more. The huge costs and numerous failures demand a bit more rigor, and that is where software engineering comes into the picture.