There are different types of print.
The OP is inquiring about PPI, not DPI, but doesn't yet know that.
DPI (dots per inch) is an inkjet print device resolution specification, not a digital image print resolution specification, which is PPI or pixels per inch.
Indeed, most inkjet prints cannot print at the same DPI resolution in both the vertical and horizontal directions.
It takes many dots to print a single pixel.
At it's most basic it takes 3 inkjet dots to print a single pixel, but a print made that way would not look very nice.
So inkjet printers today use hundreds of dots to print a single pixel.
The most basic inkjet printer has 4 colors of ink/dye - cyan, magenta, yellow, black.
High end inkjet printers have as many as 12 or so colors of ink/dye.
Inkjet printers spray ink through tiny nozzles, and are typically capable of 300–720 DPI. A laser printer applies toner through a controlled electrostatic charge, usually in a range of 600 to 2,400 DPI.
The type of print head in an inkjet printer, thermal or piezoelectric, has a lot to do with how many dots the print head makes per pixel.
Epson piezoelectric print heads have something like 175 nozzles for each print head (color of ink/dye). If one of those printers uses 4 print heads (to mix 4 colors) to print a pixel that is up to 700 dots just to print 1 pixel.
Professional high-volume, production inkjet printers range in cost between $35,000 or so up to about $2 million.
Note that most digital photographs are made using one of the many color spaces in the additive
RGB color model, while printing is done using the subtractive
CMYK color model.
When red, green, and blue light (RGB) is combined in equal amounts white is the result.
When cyan, magenta, and yellow ink/dye (CMY) is combined in equal amounts black is the result. However the black produced is not as dark as we want for a print so they also use black ink/dye so they can produce nice deep blacks.
Many consumer outlets sell chromogenic prints (C-print).
Chromogenic prints are made on light sensitive paper that has 3 layers of color (Cyan, Magenta, Yellow) sensitive emulsions.
C-prints have no dots, but the print size is still a function of the image resolution (pixels dimensions) and the assigned print resolution (ppi), but many chromogenic printers are effectively limited to an equivalent of about 250 ppi.
Once a digital image has been projected onto the paper, using either red, green, and blue lasers or LEDs, the paper is then chemically processed (RA-4 process) to develop the print.
The 2 most common C-print papers used are Kodak Endura, and Fujifilm Crystal Archive.
Most of the quick print machines (mini-labs) used in places like Walmart, Walgreen's, Staples, etc are
Fuji Frontier mini-labs.
Then there are 4-color off-set prints and half-tone prints, neither much used to produce personal, professional, or gallery quality prints..