Who would have thought that?
Unfortunately printer (and scanner) manufacturers are very unclear as to terminology and 9600 dpi sounds so much better than 300 dpi, even though 300 dpi is for all intents and purposes enough to be at the limit of what the human visual system can resolve. If I remember correctly a standard A4 / 8" x 10" print at arms length (~2x the print diagonal) printed at 270 dpi works.
There are four main variables that determine resolution and colour gamut in a print:
1. The number of inks that the printer uses; 8 inks is pretty standard for an entry level professional level photo printer. The number of inks drives gamut, more than resolution. Up to 12 different inks are used in the higher end models.
2. Droplets / Dot size - The printer can either deposit a droplet of ink (in the order of 4 picolitres per drop) or not. Some of the higher end printers have variable droplet size as well. Some produce droplets of 2 different sizes and some three different droplet sizes. A dot is determined by the number of inks + the number of droplets used per colour. As stated before, when it comes to inkjet printers, only Canon, Epson and HP make photo printers. Canon and Epson make a wide range of photo printers and HP only makes them in wide carriage printers (24" and wider). Canon and HP use a thermal print head design and have a native resolution of 300dpi. Epson uses and ultrasonic print head design and has a native resolution of 360 dpi.
3. Pigment vs dye based inks - most photo quality printers use pigment based inks, which use finely ground up minerals to produce the colours. These inks are mechanically attached to the surface of the paper. These inks are more resistant to colour change and fading over the life of the print. Dye based inks are absorbed by the paper fibres and can be more vibrant than pigment based inks. They tend to break down more quickly when exposed to UV and chemical agents in the air.
4. Paper - the medium that is being printed on has different optical properties that impact what the printed image looks like. The medium used is not always paper but can be a resin or metal. Most paper is not white, but the compounds it is coated with will affect the appearance of the final print. A matte paper tends to absorb the ink more and scatters light versus a luster of glossy paper. Matte papers tend to have a lower gamut than glossier ones. Print life is often impacted by the paper that is used; cotton rag tends to have the longest life, as long as it is acid free. Cellulose (wood fiber) based papers are often buffered to reduce the acidity in the paper to give longer print life. The paper manufacturers are generally not all that forthcoming with how their papers and coatings are formulated (unfortunately).