Well, there are a couple of areas here where there can be confusion!
Firstly, although folks in the U.S. tend to refer to threads as 'National Fine' or 'National Coarse' or even 'Sae' the threads are technically 'Unified Fine' or 'Unified Coarse'!
You are correct; however, it's a very easy mistake to make, especially for those of us old enough to have been around when other names were common. I'm guilty of it myself, even though I (should) know better.
There are a couple of very good reasons for the confusion.
First, the "UN" abbreviation itself. It's rare in the US for two letters from one word to be used in an abbreviation like that, especially related to screw threads. All of the older designations used combinations of single letters from words in the full name; e.g., USS (United States Standard), SAE (Society of Automotive Engineers), NC/NF (National Coarse/National Fine), ASME (American Society of Mechanical Engineers), etc. So, when some of us see the modern "UNC" or "UNF" designation for coarse and fine series screw threads, we automatically relate it to the older NC and NF designations.
Secondly, even decades after the Unified thread system became the official standard, fastener manufacturers continued to use the older designations on their packaging. Even into the 1990s, it was common to find new packaging with NC, NF, USS or SAE designations instead of UNC or UNF.
Here's a box purchased in the early/mid 1990s, nearly a half-century after the "Unified" standard had been adopted (PFC = Porteous Fastner Co., originally a US fastener company, now a subsidiary of Brighton Best International). Note the "NC" in the description:
I don't know when the original 'National' threads wre introduced, but it was certainly the 19th Century! After World War 2, the U.S, The U.K, and Canada got together and decided to adopt the same threads! As the U.S. threads were of 60 degree form (easy angle to generate) it was decided to use the U.S. National threads as the basis for the new standard, which was 'Unified'
Unified threads are very similar to the old U.S. National threads, so although it was a big change in the U.K. many folks in the U.S. didn't really notice, and continued referring to the threads as 'National', when they were actually slightly different! in most cases the sizes and pitches are the same, but there are one or two differences, which can cause confusion!
The original system which became the 60-degree thread form of modern times was introduced by William Sellers in 1864. It didn't become an officially adopted standard until 1907. At the time, it was called the Sellers thread, or American National Form. NC for the coarse thread series and NF for the fine thread series.
Later, it became known as United States Standard (USS) for the coarse thread series, and SAE for the fine thread series. The NC, NF, USS and SAE designations carried on long after the Unified thread system was adopted. In fact, I wouldn't be surprised if (new) packaging with the old names can still be found in some places.
Finally, Unified Threads don't use 'numbered' threads greater than No.10, after which they switch to fractional! The old National threads certainly go up to No.14, giving a much greater overlap! Again, encountering a No.14 National Fine can cause confusion if you're not expecting it!
Actually, the Unified thread form does go beyond No. 10 to No. 12; it's just not common anymore.
Page from Machinery's Handbook, 21st Edition (1979):
The asterisk means "secondary sizes."
Note even Machinery's Handbook still listed the old "NC" designation along with UNC at the top.
The original numbered bolt size system was adopted in the very early 20th Century as the ASME Standard for Machine Screws and included number sizes from 0 to 30. Sizes from 0 to 16 were the most commonly used. By the 1940s, the common size range had been reduced to 0 to 12.
A "good" hardware store will still carry No. 12 machine screws, and they're also easy to find from industrial suppliers like Grainger or McMaster.