Radha is the embodiment of pure spiritual love, the light of the universe and the beloved of Krishna. She also represents the highest within us that is yearning for our connection to the divine.
In Sanskrit, when Radha changes to Radhe (as we are doing in this mantra), we are calling out the name of the personified goddess Radha e.g. "O Radha!" or "Hey Radha!". In this way, we are asking her energy to be physically present.
Whereas singing Radha is invoking the meaning of her name. See this video for more info on the name of Radha.