"Giclee" is a slang French word chosen by an American in the early '90's to describe high quality inkjet printing. Back then several new printers were released, the iris and the Giclee Print maker (we had one of these). "Giclee" means "to spray", describing the way an inkjet printer sprays ink onto the substrate. Because the word is mis-pronounced so often (Glicee, Gilcee, Gleecay, Giggly) we prefer the term "fine art reproduction".
The quality of printing of the 90's is not a patch on the quality if the work produced today as printers and inks have improved dramatically. The Canon printers we use today leave the old Giclee Printmaker in the dust buried at the back of the rubbish heap... but it was the best of it's kind at the time.
Then along came Epson with their fancy new printers that could print faster, had more stable inks and used rolls of media instead of large sheets. We had several of the first of these machines and worked them until they dies of overuse.
it then seem all our wishes had come true when Canon released their large format printer offering 12 colours versus Epson's seven, faster again and wider colour gamut producing even better reproductions.
But we were more pleasantly surprised when Canon brought out a newer version, faster and with even better inks - that's what we use today. The print head technology has advanced so much that the printing quality is outstanding - we print at 1200 x 2400 dots per inch.
But wait... there's more... arriving late 2017, early 2018, Canon will release a new printer that has a gloss optimiser - creating even glossier glossy prints - won't make any difference to cotton rag or canvas, but glossies will be awesome!
So, back to the word "Giclee" - it's popular in the US because that's where it was founded. The Europeans prefer Fine Art Reproductions and so do we. Either way you say it, the result is the same - it's the best quality printed product, using archival inks and media (paper or canvas) that money can buy ensuring you have a product that will last as long as possible.