[fsckboy]

>MW is power, not energy

i think a more useful correction for people whose day to day lives don't require them to keep track of the difference is

MW is rate of energy use with respect to time, not total energy. The rate of energy in science is called "power"

because they both are measures of energy, and the energy/power distinction in science co-opted preexisting words that didn't have those precise meanings. Total energy is the integral of power over time, so it's not really wrong to say "this higher energy battery contains more power" in everyday speech.