Here’s the necessary clarification for non-USAmericans who are confused by how confidently USAmericans are claiming these are not the same thing: American biscuits are almost identical to British scones. But not American scones. Behold the continuum:
American biscuits:
These are layered quick breads. They are almost always baked in a round shape, and when they're not, they're baked square; you will pretty much never see a triangular American biscuit. They’re usually made with buttermilk, which gives them a nice slightly tangy flavor. They’re not at all sweet on their own, but they’re also not particularly savory, and as a result, they’re a bit of a blank slate: they pair well with butter and jam, but alternatively, they pair equally well with a savory sausage gravy. There are recipes that are firmly on the savory side by virtue of adding cheddar cheese to the dough, but in those cases, people will usually specify “cheese biscuits” or “cheddar biscuits”. American biscuits can be a breakfast food, or a lunch food, or a dinner food, all about equally.
British scones:
These are very similar to American biscuits, but a little bit lighter, and noticeably sweeter. You can have these with butter and jam (or, more likely, clotted cream and jam), but unlike American biscuits, I’d never dream of serving them with anything savory like a sausage gravy. You will sometimes see bits of dried fruit, like currants or dried blueberries, baked into them, but this isn't all that common, and it's basically the extent of weird baked-in flavorings. You will sometimes see these baked into a triangle shape, but more commonly, they are round. They’re great as a breakfast food, but they’re better with an afternoon tea; you’d probably never see them as the accompaniment to a hearty, savory dinner.
American scones:
American scones are denser, sweeter, and significantly more buttery than British scones, without the more clearly defined layers that British scones have. They are almost always baked in a triangle shape, and only very rarely baked round. American scones come in a variety of flavorings – it's not uncommon to find pumpkin spice scones, double chocolate scones, lemon strawberry scones, blueberry scones with fresh blueberries baked right in, etc. It's also not uncommon to find them glazed, like a doughnut (but usually slightly less so). You do not typically top these with butter or jam, or indeed, with anything – they are eaten as-is, as an accompaniment to coffee or tea. They are mostly a breakfast food, though they may occasional feature at an afternoon tea, if someone even has one of those, which in the States, people mostly don't.
American cookies:
American cookies are exclusively a sweet dessert. They are often baked soft, and best eaten warm, although they're perfectly fine to eat cooled, and you can certainly find shelf-stable cookies in stores (which are usually hard, rather than soft, see eg. Chips Ahoy). Oatmeal raisin cookies come the closest to the place that American scones leave off, and it isn't very close. All sorts of flavorings and mixed in bits are common, although chocolate and nuts are more popular mix-in additions than dried fruit. Glazes are fairly uncommon, but not unheard of. The archetypal accompaniment for American cookies is a glass of milk, although they're perfectly nice to enjoy with tea or coffee. They are not, however, a breakfast food. Americans do consider shortbread and gingerbread to both be types of cookies, but if you refer to "cookies" in the abstract, those aren't what people typically think of.
British biscuits:
British biscuits are like American cookies, but pretty much always hard and served at room temperature. I've even heard the opinion that a British biscuit should always be "crisp", with softness as a sign that a biscuit isn't fresh. Americans are familiar with this style of treat, and generally think of British biscuits as "the type of cookies that you get in a tin" – they're very much a thing in America, but they're considered a smaller and much less popular subset of the broader "cookie" category. Like American cookies, these are often eaten as a dessert, but they are much more commonly seen as an accompaniment to tea than the American cookie is.
Tl;dr: This is like an even more complicated version of the crisps/chips/fries thing, I’m afraid. We're simply talking about different things.
