Coal doesn't extract itself. Back in say 1800 people weren't driving or taking the bus to work so would live near their work.
Therefore settlements near mines either expanded or started. So presence of coal would have had a major effect on population density.
You can see that the distribution of coal maps closely to areas of high population density across the whole island. It might have been found in rural areas but they didn't stay rural for long.
In the early industrial revolution it was often cheaper to move industry to the coal than the other way around, hence shipyards at Methil and Burntisland. Not on the scale of the victorian ones on the clyde, but heavy industry nonetheless.
So the presence of coal is associated with the presence of heavy industry.
My understanding of the phrase "central belt" is that it refers to the coal mining and heavy industry regions of central scotland, so the presence of quantities of coal would meet that definition and mean that the place is in the central belt.
Other people clearly have different views of what the phrase means.
Thanks for trying to explain to the less able though, it was a good effort and you tried really hard.