What is the difference between ADXR and ADX?

I'm curious to know, what exactly sets ADXR apart from ADX in the realm of technical analysis? Could you elaborate on the key distinctions between these two indicators, perhaps highlighting how they differ in their calculations, intended uses, and the insights they offer traders? I'm particularly interested in understanding how the smoothing process inherent in ADXR might affect its reliability compared to ADX when identifying trends and potential reversals in the market.