Pigment is completely different to dye, but some printers can use either types of ink. Yes pigment is more expensive.
Pigment - longer lasting, more resistant to fading. Better for transparencies. NEGATIVE - colours not as bright as dye.
Dye - doesn't last as long, so not suited to archival as much. POSITIVE - brighter colours (when fresh). NEGATIVE - a drop of water makes it run.
My general advice - if printing photo's that won't be overly exposed to sunlight or that don't need to last forever - CHOOSE DYE.
If you want to print on unusual media types such as transparencies, or you want to print things like a contract that you wish to have a good life - CHOOSE PIGMENT.
If you need to always do a mixture of everything, stick with dye every time.