To take a popular Canon cartridge to use as an example, the CLI-8BK Photo Black cartridge uses a dye based ink (ChromaLife 100 Year). Dye particles are smaller (thank pigment), and tend to lay flatter meaning that they are more vibrant, and do well on glossy papers.
The other black cartridge in this series is the PGI-5BK cartridge. This cartridge uses a pigment ink, which is an insoluble substance. These inks have a significantly longer lifetime than dye inks and tend to be more controllable than dyes.
Whilst pigment –based ink doesn’t set well on coated paper, it is generally the best choice for matte paper (where dye based inks get absorbed too much, leading to washed out colours. This makes it better choice for text prints!
So there you have it. Two black cartridges. Two different types of ink. Two different purposes!