ERS Management refers to how the energy is being used, either deployed ore regenerated.
The teams have various modes for this. You can have high deployment, low deployment, high regeneration, low regeneration, balanced, top speed, overtake, etc. The teams all have different versions of all of these, depending on how they need the car to handle.
The reason for all these different modes is how the energy is being harvested and distributed. You have energy coming in from the MGU-H, and MGU-K, and either going to batteries or deployment to produce more power.
Battery deployment purely refers to the battery being used to create more power. This can either be from the engine mode - for instance, high deployment or hot lap mode, or using the overtake button.