At the same time, the most common form of 'charcoal' that an average person will use in their BBQ is made from both charcoal and coal, as well as other things.
You’ve repeated this a few times, but I clicked on several charcoal options on Home Depot’s website, and they claimed to be made entirely of “100% natural hardwood”. Maybe some cheaper ones have added coal?
Take Kingsford, for example, probably the single most popular brand of briquettes at Home Depot. It does not say 100% natural hardwood, it says 100% natural ingredients, including wood. Coal is natural. And 15-40% of Kingsford briquettes [0].
They do often contain coal. Briquettes are weird. For smoking, you really want to be using wood (or charcoal and wood); charcoal has most of the volatiles burned off already, in principle leaving behind only carbon, so it isn't great for smoking things.
> "Kingsford Charcoal is made from charred soft and hardwoods such as pine, spruce, hickory, oak and others depending on which regional manufacturing plant it comes from. That char is then mixed with ground coal and other ingredients to make a charcoal briquette. As of January 2016, Kingsford Charcoal contains the following ingredients:[7][8]"
"Research and patent literature show that when charcoal briquettes are produced using an organic binder such as anthracite, the binder is present in quantities of between approximately 2 and 8% by weight."
And "coal, anthracite" is clearly listed as the third most common ingredient in the safety sheet for Kingsford Charcoal Briquettes, after charcoal and ashes.