In civilian aviation, these two terms are used interchangeably and essentially mean the same. They both can be abbreviated as "Rad Alt" sometimes as well.
This system measures the between an aircraft and the ground directly below it. "Radar" or Radio Detection and Ranging is the principle by which the system operates. That is, a signal is transmitted towards the ground and then received back for processing. The time the signal takes to reflect back to the aircraft is timed and this is how the altitude is measured. The signal that is transmitted is a radiowave. Thus, this is perhaps this is the reason why some may use the term "Radio Altimeter" instead of "Radar Altimeter".