Question's in the title; what makes Computer Science Stack Exchange differ from Theoretical Computer Science Stack Exchange?
Theoretical computer science is for mathematicians working in the field of theoretical computer science, at the level of graduate student and upwards. It accepts only research-level questions.
Computer science, in contrast, is for all levels of theoretical computer science, defined somewhat more broadly than in TCS. Many questions here are homework exercises, though some are genuine questions by undergraduates or by working professionals outside academia, or more rarely more basic questions by experts. Some of these questions (both by undergraduates, by professionals, and by post-graduates) are difficult enough to merit asking in TCS.