Rocks can be countable too, although ‘rocky’ might mean a continuous area or patch of ground made of ‘rock’, which wouldn’t be.
I’ve now started thinking about standing stones such as Stonehenge… definitely not liftable and I wouldn’t refer to those as standing rocks.
So in conclusion, I have no idea!!
Yeah, same with me. In between the houses here, the spaces are usually filled with a sidewalk, and a plot of pebble-sized rocks beside it. They are rough, and I’ve never heard anyone call them “stones” around here. Like I said, we always threw “rocks” at stuff as kids, and, come to think of it, all these “rocks” were jagged, imperfect things. To me, stones were the bigger, smoother, more decorative rocks you might line a boundary with.
Speaking ex cathedra from the seat of my trousers, I speculate that the difference, at least in English, is smoothness - a stone is a smooth rock.
Consider the metaphorical uses of the two words; a stonefaced person is impassive, emotionless, blank. Whereas a rocky countenance is uneven and rough. Getting stoned is a mellow experience; getting rocked is not.
I suspect the connotation of “smoothness” underlies the distinction between stone, shaped for a purpose - e.g., a stone bridge - and rock, in its natural state - e.g., a rock layer.
Just my SWAG.
Speaking from the equivalent location, I think you might have something there.
That’s absolutely not how that distinction works in my dialect of English. Rocks, as a countable noun, are absolutely something that you can pick up (and throw).
Charlie Brown backs me up on this.
Fair enough, each to their own! I would always think of throwing stones (e.g. people in glass houses shouldn’t, etc), could be a local thing, or maybe just a me thing!
Google ngram suggests that “throw a rock” was rare everywhere until about 1900, and still rare in British English until about 1980. That’s in accord with my personal recollection - I think it’s was definitely “throw a stone” when I was growing up in the U.K., whereas I’d associate “throw a rock” more with American dialects.
We may throw a rock, but something is just a stone’s throw away.
What the hell would you know about it? 
Sort of like this?
I think of stones as being smooth and rounded, and rocks as having sharp edges. One can skip stones off water because they are smooth.
Stone tools are smooth so that you may hold them in your hand. The problem arises with cutting “stone” tools, usually flint, with sharp edges.
When diamonds are called “rocks” as slang, the slanginess, the implicit humor, means the speakers are aware on some level that the only proper designation for diamonds is stones, like all gemstones. So calling them “rocks” is deliberate ironic humor and speakers who use that slang are, I think, aware of it.
Now how about when a drink is “on the rocks”? Ice cubes are smooth-surfaced artifacts entirely formed by human hands for human use.
I think “on the rocks” for a drink is figurative - evoking a stream or waves splashing over rocks.
The phrase comes from when people didn’t have ice makers in their homes, and instead would have a big slab of ice delivered regularly to their front door. If you wanted ice for a drink, you’d get out an ice pick and chip off a few chunks, hence “rocks” instead of smooth, stone-like ice cubes.
All of the above goes to show a strange semantic situation, where two words almost totally overlap in meaning, and yet maintain a distinction with some kind of difference. Even no there are no clear guidelines for which is which, and consciously we don’t differentiate, on some subconscious level we’re aware of two overlaid semantic ranges instead of just one.
In my experience, there is a similar complex relationship between say and tell. In my decades as a journalist and editor, I had a lot of trouble explaining to writers why it was mostly appropriate to use said and only sometimes appropriate to say told.
In my mind that’s an easier distinction. “Said” is just “the words came out of someone’s mouth”, while “told” implies those words also landed (intentionally) on someone else’s ears and they understood, or at least they should have. A person can “say” something entirely by themselves, buy they can’t “tell” anything without a someone else present.
(Expects at least half a dozen dopers to point out a dozen common turns of phrase where that is not the case)
In India I noticed that say and tell correspond to only one verb in Hindi, kahna, and the two were interchanged frequently in Indian English.
In my editing experience I got really tired of writers replacing “said” with “advised.” No, “advised” is not a synonym of “said.” How did that even get started?
Mmmmh, this gives me an idea for a thread…
The French common noun la pierre and the personal name Pierre are both from Greek: petra for the former and Petros for the latter. La pierre crossed the categories from rock to stone in French, because of course the semantic boundaries are very fuzzy.
The name of ancient Petra in Jordan, rose-red city half as old as time, directly means ‘rock’ in the sense of my OP: it’s carved from what is called the “living rock”—meaning specifically the Earth’s crust.
“But from the rock as if by magic grown” (J.W. Burgon)