Q:

What are the differences between operating systems and computer systems?

Wikipedia's definition of a "computer system" is:

Computer system is define as the combination of hardware software user and data with referring to communication and procedure involved in between them.

Which doesn't make much sense to me. Whereas the definition of an operating system is:

An operating system (OS) is system software that manages computer hardware and software resources and provides common services for computer programs.

Both those definitions seem to refer to the same thing: a system that manages hardware and software for controlling programs.
A list of topics doesn't help me much, either. For example, MIT's computer systems course lists the topics as:

virtual memory
threads
networks
atomicity
coordination of parallel activities
recovery and reliability
privacy, security, and encryption

While MIT's operating systems course lists the topics as:

virtual memory
threads
context switches
kernels
interprocess communication
interrupts
system calls
coordination
interaction between software and hardware* 

*According to the only answer to this question, this is a computer systems topic?
It seems like OS is slightly more related to software and to individual computers, whereas computer systems might involve multiple computers?

A:

Both those definitions seem to refer to the same thing: a system that manages hardware and software for controlling programs.

No, the first definition says "a computer system is a combination of hardware and software, not it manages the latter. That means a computer system includes both - the hardware (processor, main board, various kinds of memory, gfx card power supply, peripherals etc.) plus the software  called operating system which manages the former. The term "computer systems" does also refer to systems build up from many computers, which are interconnected by a network.
Since operating systems ("software") are always part of a computer system ("software + hardware"), and they do manage hardware resources, it is not too surprising that the MIT course on computer systems covers also some aspects on operating systems. I do not know those courses, but from the title and the topics list I would expect them having some overlapping parts, but a different focus.

