Capacity (kWh) is how far a car can drive — the total energy stored. Power (kW) is the speed limit — how fast energy can flow out. A big battery with low power is a truck with a huge gas tank and a 25mph governor: lots of range, can't run the heavy stuff.
Heavy appliances — AC, pool pumps, EV chargers, dryers, heat pumps — need high power (generally 5kW+) just to switch on. They also drain capacity fast. This is why battery specs matter more than brand names: a Tesla Powerwall 3 (13.5kWh / 11.5kW) and an Enphase 5P (5kWh / 3.85kW) are built for completely different jobs, and both are excellent at their own job. Batteries stack like batteries in a remote — two 10kWh units = 20kWh — so systems are built from the load up.