In the early days of photography photos were not printed but they were developed. There is a big difference between developing a photo and printing a photo. Developing photos was a chemical process in which photos taken on film were put on what is known as photo paper. Developing photos is a complicated process that involves many stages and many chemicals. Although you technically can develop photos at home it is too complicated process for most people and requires a special setup. You will need a dark room special equipment and special materials such as photo paper and chemicals.
Printing photos on the other hand is a clean process the only chemicals involved are embedded in the ink used which is usually enclosed in clean small cartridges. Printing digital photos can be done on regular or special paper and you can do it at home easily with equipment that costs as little as a few tens of dollars. The way photo printing works is very different than how photo development is done.
To understand digital photo printing we should first take a closer look at what digital photos are. Digital photos are files stored on computer storage that include a description of a photo. The description is comprised of many pixels each with its color and intensity information. If you would zoom into a digital photo you would notice that it is built from many pixels usually in the millions. When put next to each other the pixels create the illusion of a photo since our eyes cannot separate each pixel but instead merges them all into one photo.
Digital photo printing is based on the same concept. If you were to print all the digital photo tiny pixels next to each other and then look at the printed result you would see a photo for the same reason since your eye can not separate each tiny pixel but instead merges them all to create the photo picture in your head. Digital photo printers in essence are very simple. A computer is connected to the printer and sends printing information which is in its core a long list of all the photo pixels with the intensity and the color information for each pixel. The printer then takes that information and for each pixel puts a corresponding pixel on the paper. The result is a printed digital photo.
But the digital photo printing process is easier said than done. In order to be able to print each tiny pixel accurately on the paper many technologies had to be developed and ready. For example accurate motors and feedback systems are needed in order for the printer to position its printing head on the exact place over the paper where the pixel should be printed. To print the pixel the printer should be able to apply the right ink at the right amounts to create the right color and intensity. To do that enough computer power to run color conversion software is needed in the printer. To be able to print tiny high resolution pixels ink cartridges had to be developed that can accurately and very fast inject ink at very small amounts. Moreover the ink heads need to be controlled electronically since any mechanical control would slow down the printing process.