Then when you cover with ink the raised surface of wood that is left and press the paper upon it, the design prints off in black where the ink is but the paper remains white where the hollows are.

This is the method called wood-cutting, which is still in use for book illustrations.
In the other process, the design is ploughed into a metal plate, the lines being made deep enough to hold ink, and varying in width according to the strength desired in the print.

You then fill the grooves with ink, wiping the flat surface clean, so that when the paper is pressed against the plate and into the furrows, the lines print black, out of the furrows, and the rest remains white.
There are several ways of making these furrows in a metal plate, but the chief are two.

The first is to plough into the metal with a sharp steel instrument called a burin.

The second is to bite them out with an acid.