Inkjet is the generic term for printers that spray ink droplets onto paper with thermal jets. Deskjet is just HP's name for their inkjet line. Most of the inkjet printers out there (including HP) use the thermal jet design, only Epson has gone its own way with their piezo jet technology. The only drawback to Epson's design is that their piezo jets are finer than most thermal jets, so the jets tend to clog easily if you don't use the printer a lot.
.bh.