As noted the power has to be defined as energy divided by time
Heat power in IP units is BTU per hour
Heat power in SI is Joules per second. Joules per second is more commonly know as Watts.
Energy on the other hand is exactly that.
A KWh is just a useful unit so that people can get a grasp on what energy is being used over a set period. This can and really should be just called Joules. So 1KWh is actually 3.6 million Joules. That sounds like a HUGE number and once you get into big heat power it can make it look too big and then people make errors as to whether it is MJ, GJ, TJ
Because heat power in IP is in BTU/hr, to equate a KWh simply means converting Joules to BTU
So 3.6 million Joules is 3,412 BTU.
So it is the same thing, but just common usage has replaced some of the correct technical definition.
Remember - More details = better answers
Also: If you get a response it's polite to respond to it.
Also, as a clarification: Btu/hr is often written as Btuh. Hence your conversion from kW to Btuh (which is Btu/hr) is dimensionally consistent. kWh is actually kW*hr (analogous to Btu as a unit of energy), making the notation inconsistent with Btuh.