Today we had a couple of hours of heavy rainfall, and when it stopped
raining the water level in my pond had dropped four inches.

I know that water moves through the kiddy pool part of the filter very
slowly, and that it stays so full that lots of rain will cause it to
overflow. My question is, when the kiddy pool overflows does it just spill
out the excess rain water or dies it also spill pond water too, and thus
cause the drop in the pond level?

I'm not even sure that question makes sense... Sorry,