Requirements management is more generic. All projects have some requirements eventhough they may not necessarily have anything to do with engineering. Requirements engineering mostly refers to the software/system engineering related processes.

The requirement management is a broad area since that is one of the parts of the Software development steps. Since it is more generic and the step is always there without absence. If you take the engineering the indeed you have to obey some basic principles of the engineering such as "theory", "method",  and "tools". So If you want to get in to requirement engineering, then you need to apply the theory you learned about the requirements through a best method to either collect or understand with the help of the technology tools you have. (hope i answer the question)