Yes! So it's a little like that. You put inkwells of different color on a bar, it moves across the paper and mixes colors to create the image. It sprays very tiny dots of ink to form the picture.

As for how it knows what the picture is, it has to communicate with the device that took the picture. Sort of how the shellphones talk to each other. The printer has the job of figuring how to translate that picture into the tiny dots of color.

You can get away with just four different colors of ink; cyan, magenta, yellow, and black. More complicated, you add orange and green.