There is a difference, but the image pixels map to the printer pixels quite nicely. I'm going to simplify a bit and I'm not going to be pendantic and with refer to black as a colour, even though it's not.
Let me stick with the Epson Stylus Pro 3880, that I know quite well. It has 8 different ink colours (black, gray (Epson calls this Light Black), light gray (Epson calls this Light Light Black), light magenta, magenta, yellow, light cyan and cyan). Just to confuse things a bit, there are two blacks; one (Photo Black) is used for glossy paper and the other (Matte Black) is used for matte papers, but only one of these is used for a print and the printer selects which one based on paper type in use).
The 3880 can also deposit two different dot sizes; a full sized dot and a half sized dot, so the printer can generate additional colours by varying the dot size. In the highest quality mode, the printer deposits 2880 dpi using the 8 "colours", so 2880/8 = 360 dpi, which is the "native resolution" of the Epson printers. Canon and HP printers run at 2400 dpi, so 2400/8 = 300 dpi resolution.
So, the mapping between the pixels in the file and dots on the paper do line up; one colour pixel in the image maps to 8 discrete ink dots on the paper. If you set your native resolution in your image file to be the same as the printer resolution, the printer driver does not have to do any interpolation, hence the recommendation of using file resolution of 300 ppi for images to be printed on Canon and HP printers and 360 ppi for Epson printers all makes sense.