The difference between the two sites is the difference between computer science and software engineering.
Programmers is focused on the practical aspects of building software - requirements, architecture, design, testing, deployment, configuration management, software quality, process and project management. Things of unique interest to software engineers are also on topic - software licenses, business aspects unique to software development.
Computer Science is more theoretical and mathematical in nature - programming language concepts, languages and grammars, complexity theory, computability.
There is, however, some overlap. For example, there may be a set of data structure or algorithm questions that can be asked to either community. However, the answers you get would vary. Here on Programmers, I would expect answers to be more concerned with a different set of trade-offs than on Computer Science - ease of implementation, maintenance, testability, the existence of well-used implementation versus time and/or space complexity.