What printer model? In general, the ink cartridge is the part that contains the ink, the printhead is the part that has the nozzles that spit the ink onto the paper.
Some printers such as the Officejet 6830 have separate ink supplies and printheads. These printers typically have four or more individual ink supplies, one for each color. Some printers, like the Officejet 6830 have the printhead fixed in place. Other models, such as the Officejet 8620 have removable and replaceable printheads.
In some printers such as the Officejet 8040a the ink supplies and printheads are integrated, the ink cartridge also includes the printhead. These printers typically have a black cartridge (with printhead) and a separate tri-color cartridge.