The CleanPower boards are circuits designed to replace the power voltage generation of the consoles. For example on the Game Boy Original it replaces the power board that takes the battery input voltage and creates the 5V system voltage and the negative LCD bias voltages.

For the Game Gear, the CleanPower replaces the power board and takes the battery input voltage and generates the 5V, 9V, 1.28V and 34V for the system voltages and LCD bias voltages. 

The CleanJuice boards differ in that they are designed to replace the actual original power source, such as AA batteries, with Lipo batteries, and include all of the Lipo battery charger circuit, USB-C connection for charging and powering, and sometimes (like in the case of the Game Gear) can replace the power regulator circuit at the same time.

For the Game Boy both CleanPower and CleanJuice can be installed. 

For the Game Gear, the CleanJuice already does the job of the CleanPower as well as the Lipo battery, so only the CleanPower or CleanJuice is needed. CleanPower to keep AA batteries and add USB-C power capabilities as well as a new power board, or the CleanJuice to replace the AAs with Lipo batteries and the power board replaced with a new one including USB-C charge and power.