Here are shortcuts to the two help articles explaining each. In short, the Robot Manager component can only connect to the Robot Manager instance whereas the REST Client can connect to any REST service.
Robot Manager REST Client can, through Robot Manager ( with the queue control and all benefits of Robot Manager), Make my automation called by REST service. Sending requests and getting responses as a usual REST Service. I'm asking this cause i'm working on a Robotic solution that gets data from a Mainframe and it shoud return it back as a Json file. Do i understood correctly?
I got the REST Service concept, i'm already using it to get data from a rest service.