My understanding is: a Remote Indicating Compass is a system that provides magnetic heading information to one or more instruments, utilising a flux valve located remotely to minimise aircraft induced magnetic anomalies, whereas a Radio Magnetic Indicator is a specific instrument used to display ADF and/or VOR bearing information, utilising magnetic heading data supplied from a Remote Indicating Compass system.
This site explains it well, in particular the last paragraph:
https://aviationtheory.forumotion.ne...cating-compass