Here is my $.02 FWIW.
My favorite analogy involves working on an old car motor:
You have a big, long wrench to loosen a rusted head bolt. You put the wrench on the bolt and pull for all you are worth for about 10 minutes (until you are sweaty and sore) but don't move the bolt at all. THAT IS THE EQUIVALENT OF AMP HOURS.
Then you get smart and spray on some PB Blaster and let it set overnight. Next day you put the wrench on and with one pull, you loosen the bolt. THAT IS THE EQUIVALENT OF WATT HOURS.
In the first example you did NO work. You may think you did. You may feel like you did, but you didn't.
In the second example, you did work.
The word "WORK" here is the scientific or physical definition of the word