My own understanding is as follow, happy to stand corrected....
RFI is interference that affects radio frequencies. It is not necessarily caused by radio transmitters, it often radiates from (for example) badly designed or faulty switch mode power supplies, among other culprits. Radio transmitters operating within legal frequency and power bands emit RF energy, but that is intentional, it is not RFI.
REIN, by its acronym, is impulse noise, such as may emit from the spark generated by the brushes of an electric motor.