Energy Rate, or Power, is Watts (joules per second) or kW for 1000 of them.
Battery Capacity (also electricity usage as billed by your power company) is how much power you can use for a certain amount of time - that is, kiloWatt-hours (kWh). If you could "floor it" with a 120kW motor for 30 seconds, you will have used 1kWh of battery energy/capacity, give or take. You might reach software limited speed by then but just using it as an example to get round numbers.
Your charging rate is power, not total energy, so it is in kW, not kWh. The onboard AC charger is 6.6kW if you find a J1772 station capable of outputting that or higher. Some stations are 5kW. The actual "charger" converting AC current to DC and sending it to the battery, is inside the car. The fixed "charging station" hardware is just a 220 volt AC conveyance that provides a certain level of power (5kW or 6.6kw or more since there are other EV's that can handle more AC power).
A Chademo DC Level 3 charging station (your local Nissan dealer perhaps) puts out about 380V and 50A of power, if your battery charge level is not very high - the amperage (and power) sent to the car decreases as the battery fills back up, as you saw.