Giclée was the first word coined for modern printing, so it's often used to describe any modern print. The main - if only - difference in Giclée and Pigment printing is the type of ink used. Giclée's were printed with a wet (liquid) dye ink that absorbed into the paper rather than dry pigment ink (using powdered water) that sits on top of the paper.

Note: Giclée's are also referred to as Iris Prints, because they were made on Iris Printers, whereas Epson, Canon and others make today's printers.

What is the Difference between Dye and Pigment Inks?

Dye is pigment fully dissolved into its liquid carrier, whereas pigment remains in its natural dry powder form and doesn't dissolve into its powered water carrier. That's important because pigment is dry when it hits the paper, so it doesn't absorb into it. Pigment remains - or sits - on the surface of the paper. And the colors are brilliant.

Are Inkjet Prints Different? 

The term Inkjet Print technically could refer to prints made either with dye or pigment ink, but most artists consider the term to denote the use of dyes rather than pigments.

Note: If you're wondering how pigment can be described as having a liquid carrier yet 'go onto the paper dry,' its because the force of the inkjet momentarily 'liquifies'  the powered-water carrier, but the process essentially remains dry.