When I worked in the past to find a source to sell me those Bic orange medium fine point pens, I ran into a nomenclature issue. When it was rolled out in the 1960s, I remember it was called a medium fine point; there was a white barreled pen with a metal clip called an Accountant extra fine point. I didn't like that pen; the point was too sharp and it had a tendency to either jam the paper or smear.
Apparently, over the years, the Accountant fine point was one of the pens that contributed to the stereotype of nerds who had ink stains on their shirt pockets. I suppose because the tip was so small, the pen ink well must have had some extra pressure to force the ink to flow - which led to its propensity to explode.
As the years went by, to the best of my knowledge, the Accountant fine point was converted to the same ball size as the medium pen - .o8 mm - and they were both dubbed fine points. The difference with the Accountant was then stylistic - it has a white barrel and its plastic cap lacks the "clip", it still has a separate metal clip.
Bic still makes a pen with what is called the needle tip - .o5 mm - but it has a totally different design.
When I first began looking for a source for the orange pen, I didn't realize that for most of its existence it was called a fine point; when I was a kid, it was still called a medium fine point.