From "Sanding and Planing" by Nick Engler:
"Files are classified in three ways -- by how coarse or fine they cut, by their tooth pattern, and by their shape.
"Cut -- The way in which a files cuts is determined by the spacing between the teeth. The more teeth per inch (tpi), the smoother the cut. The teeth on comon files vary from 14 tpi (the coarsest) to 100 tpi (the finest) Manufacturers rarely label their files according to tpi, however. Instead, they divide them into threee broad (and somewhat arbitrary) grades. From coarse to fine, these grades are
bastard cut, second cut, and
smooth. You can sometimes find additional grades among older files --
rough, coarse, dead smooth, and
dead-dead smooth. Coarser grades cut quicker, finer grades cut smoother. Extremely fine files don't cut wood worth a darn because the teeth clog too quickly. These work better on metals.
"Tooth pattern -- The teeth are cut into files in two different patterns,
single-cut (parallel cutting edges) and
double-cut (crossed cutting edges) Of the two, the double-cut pattern usually works better in wood. Unless they are fairly coarse, single-cut files are better suited for metalworking.
"Note: On most files, all the surfaces have teeth. But a few types have one or more
safe edges, without any teeth.
Shapes -- Files are available in many different shapes -- flat, round, half-round, tapered, triangular -- and these shapes often come in different sizes, with a variety of cuts and tooth patterns as well. Refer to "Files and Rasps...for an illustrated list of the common shapes."
By the way,
"mill" refers to the shape
and tooth pattern of a common file -- single-cut, rectangular cross-section, tapers along the width and thickness. It may also refer to the cut as most mill files are either bastard, second-cut, or smooth. A rough or coarse mill file was once commonly called a "float."
If you'd like to have the illustrated reference referred to in the book, I've attached it as a .pdf file --
http://www.shopsmithacademy.com/Files&Rasps.pdf --
RIGHT-click on the URL and choose "Save Target As" or "Open in New Window." The file was too big (1.2M) to upload to the Forum.
With all good wishes,