What is the difference between DMI and ADX?

Could you please elaborate on the key distinctions between the Directional Movement Index (DMI) and the Average Directional Movement Index (ADX)? How do these indicators differ in their purpose, calculation, and the insights they provide to traders? Are there any specific scenarios where one might be more suitable than the other? I'm particularly interested in understanding the nuances that set them apart in the realm of cryptocurrency trading.