Not in this country, Pro. Biscuits are something else entirely, as any self-respecting southerner could tell you. (Where's skipvia, anyway?) But in the U.K., Australia, and presumably some other places, what Americans call cookies are actually biscuits.
Real biscuits are soft--made of flour, butter, milk, and nothing else--and are served hot. If you are served biscuits in a Southern restaurant and they get cold, you will be brought a basket of hot'uns.
Some cookies are soft and a few are hard. A Ginger Snap is an example of a hard cookie. On the whole, I guess I'd say that most cookies are soft and chewy to crisp. I think most Americans think of a biscuit as more of a bread product that a dessert.
Several of the Harry Potter books came out while I was in the States, so I dressed up in my black opera cape and went to my local bookstore at midnight and bought them there. One year, on a visit to Australia, one of my niblings wanted the latest book in the series, so naturally I bought an Australian edition, which gave me a chance to compare.
There is one scene where McGonagall offers Harry a biscuit from a tartan tin (with British/Aussie readers assuming something crunchy, possibly, in the context, a shortbread biscuit). The exact line is something like: "Have a biscuit," she said, pushing a tartan tin towards him.
In the American edition (and I admired this for its deftness as well as refusal to completely kowtow) it read: "Have a biscuit," she said, pushing a tartan tin of cookies towards him.
It's deft in that McGonagall is not given a line that she would never have uttered, but at the same time the little American readers weren't left thinking that she was offering Harry a hot scone.
To answer the original question, I would consider biscotti to fall more or less into the British/Aussie biscuit category (although I'd use the Italian name here in Australia because they're not quite like ordinary biscuits either). Would Americans consider biscotti "cookies" I wonder?
PS. Notice they didn't try to translate "tartan" to "plaid"…
Well, I'm American, and I'd definitely call biscotti "cookies", based on the following reasoning: Biscotti are sweet. Cookies are sweet. Biscuits are savory.
Actually, I'd argue that in the US, we draw a three-way distinction:
Cookie: small, flat, sweet
Biscuit: fluffy, savory, good with butter and jam
Scone: not fluffy but not flat. Dry. Kind of like a triangular brick made of flour. Often sweetened.
Wikipedia agrees with me. "In the United States, scones are drier, larger and typically sweet. Those sold by coffee shops often include fillings such as cranberries, blueberries, nuts, or even chocolate chips."