One little, important detail:
You talk about 200 Watt/hour (watt PER hour). This is INCORRECT!
It is 200 Watt-hour; that is, 200 Watt TIMES hours.
When you express the units correctly, you suddenly find that that old highschool math is all you really need...
An ENERGY of 200 Watt-hours equals using a load of a POWER of 200 watt DURING 1 hour
or
the POWER of a load of 20W load DURING 10 hours
or
a 1W load DURING 200 hours.
I.e, wattage times hours equals Watt-hours.
(POWER * time = ENERGY)
(CURRENT * time = CAPACITY (of a battery))
Suddenly, kWhr (kiloWatt-hours) makes sense too
The same goes for the capacity of a battery, in Ahr (ampere-times-hours; NOT ampere/hour); a battery with a CAPACITY of 7Ahr can deliver a CURRENT of 1A during 7 hours; or a CURRENT of 7 amp during 1 hour; etc.etc., ad nauseam.
No worries, the mistake you've made (watt-per-hour) is a very common one. And it obscures a real understanding of this unit and its proper application.
Start applying the correct units, and you'll find that those high-school physics are actually useful in the real world too