The difference is in the kind of ink particle...the dye or pigment. In your case, PGI-* are pigment inks, and CLI-* are dye (ChromaLife 100 year) inks.
Dye inks use dye particles, which are soluble substances. Dye particles tend to be smaller than pigments, lay flatter on the surface of papers, and are often a bit more vibrant in the way they reflect light (which can actually be a detriment, rather than a bonus, when trying to print color-accurate photos.) Dye inks tend to do quite well on glossy papers and do not usually exhibit gloss differential. Dyes, as they are soluble, tend to have shorter lifetimes.
Pigment inks use pigment particles, which are insoluble substances simply suspended in solution. Pigment particles are larger, and can often lay unevenly on paper. Pigment inks can also exhibit certain effects such as metamerism, bronzing and gloss differential, however these days pigment inks are highly advanced, and such problems are mitigated to their minimums. Pigments also tend to be more controllable than dyes, and an extensive range of pigment inks is available for high quality pigment-based ink jet printers. Gamut and overall color quality that can be achieved by full pigment ink printers is second to none these days. Pigments, being non-soluble (and given their significant technological advances over the recent years), tend to have significantly longer lifetimes than dye inks.
The particular printer you have is not really known as a high quality photographic printer in the grand scheme of things. It probably has a pigment black ink to improve the permanence of text printouts, and possibly to support matte papers better (which have a tendency to absorb dye inks a bit too much, washing out the color.) The dye is probably used to support gloss better, as pigment ink usually causes a gloss differential...if pigment black is used on gloss with the dye colors, it usually leaves quite noticeable gloss differential for all the black (text, lines, etc.)
The two black cartridges you are referring to fall into two main categories: Pigmented and Dye-Based Ink. Your PGI-220BK is pigment based and your CLI-221BK is dye based.
Dye-Based Ink Advantages:
Pigmented Ink Advantages:
The type of paper you are using, the final presentation, and the artistic feeling you are going for all contribute to which type of ink you will prefer.
Graphic and fine arts are much more likely to use pigment based inks because they are much more stable and can last more then 200 years on some paper types.
In photography specifically, the decision typically comes down to the printer design. If your printer supports both, you will find that using pigmented inks for fine art presentations on specialty paper might be the best option. If you want a print to be ready quickly and not necessarily last 200 years, while considering the cost of the ink, you might find dye based inks to be the best choice.
PGI-* are Pigment inks, CLI-* are the new ChromaLifeInks which are dye based. They're two very different inks.
The difference I suppose is that I sometimes print on paper with the color-on setting and sometimes on paper with the grayscale-on setting and it chooses the black with color cartridges and the one without for monochrome.
But then it begs the question: how does this interact with the paper (doc) vs glossy (photo) choices?
I purposely choose color for most by default because I like the information to be identical (alike to the web page I'm viewing).
But if/when I just want black and white I choose the greyscale setting.
This strategy seems to get me even use and I end up replacing the cartridges close to the same time. Ummm... although I see I have a spare CLI-B221K so I guess I'm printing more color documents that don't have "enough" black in them! :-)
Am I close to right???