There is no question with darkroom systems and photographic papers.
It is quite different with digital printers.


The size of a digital print depends on the number of pixels of the digital image, and the number of pixels per unit of length. This is not at all related to the printer settings which decide the number of dots of ink by pixel.
Dots of ink and patterns:
All printers need several dots to print one pixel, depending on printer technique. Note that dpi is for dot per inch and shall be different from ppi, pixel per inch. For example, a 256 scaled grey pixel will require 8 dots or micro-drops of ink with an ink jet printer. The soft of the printer calculates and defines the number of dots, the size and the location of each dot depending on the printing options that can be set in the properties of the printer. Thus, each pixel is printed with a pattern of ink drops.
The maximum number of ink dots indicates the ability of the printer to produce quality prints. It varies depending on the printer technique.
A pixel is equal to one pattern of micro drops.
In a ink jet printer, the dot is a micro-drop of ink.


Nonsense related to digital printing:
In professional printing of magazines, books, etc, the number of lines of patterns per unit of length is used for defining printing conditions.
There are many patterns depending on the printing techniques.
Unfortunately for amateurs, in the window for setting the print size, most softs are indicating dpi when requesting the number of pixels per inch when it should be shown ppi.
Of course it is wrong and really confusing. Now, that way is so commonly used, for scanners and printers, and the number of ink dots being impossible to set but necessarily calculated by the soft and unknown by the user, it can be guessed that dpi shall be read as ppi and is no more related to ink dots.