I had the same question when I started out my career in Computer Science. Based on my understanding I could say C.S develop the actual programs and IT troubleshoot those programs.
Computer Science is the design and development of software, operating system, games, web and related hardware. It would involve the use of complex algorithms to solve our daily needs. Often called business analytic or business intelligence (B.I) which is nothing but say a manual that comes with a new product (say camera) and depending the needed functions it follows a guided number of steps. Now a days, efforts have also been put in technology to learn by itself say search engine learns what you want before you even tell it entirely.
Information Technology is development, maintenance and use of already existing software, network, operating system, web framework to create a larger application. It monitors the information system and system administration. Due to its business specific needs, IT workers may interact more with customers. Example NW Admin, Database Administrator, System Administrators, Analyst, Architects, etc.