And just to make sure we're on the same page, I think the OP was asking if in that last example you gave, would the SOG be 200 mph or 181?
From your flying experience it sounds like it would be 200.
It's actually difficult to find a definition for SOG that ever even mentions vertical velocity. However, I think I found something relevant at this link
, supposedly a glossary of terms for avionics systems. Notice that it makes a distinction between "Earthspeed" - the velocity in the direction parallel to the Earth's surface directly below (which is exactly what a car's speedometer is measuring) - and "groundspeed" which is explicitly the horizontal component
of travel (i.e. The earthspeed vector projected onto a horizontal plane).
I realize that "groundspeed" may not by definition be the same as "speed over ground", as well as the fact that reading something on the internet doesn't necessarily make it true.
However, it does lend credence to the OP's hunch that SOG really does just refer to the horizontal component of velocity.