The essential difference is that giclée prints are pigments on paper, whereas photo prints are exposed onto light-sensitive photo paper and developed chemically.
Giclée prints consist of tiny dots of color passed on cyan, magenta, yellow, and black (CMYK). High-quality printers, for example, also use additional light versions of these colors. All of the colors in the printed photo are then mixed from these colors, with very fine drops of inks next to each other on the paper. If you look extremely closely (through a magnifying glass, for instance), you can see the individual dots of color. This is called a halftone pattern.
Photo prints do not have halftone; there are no dots. The photo paper is exposed by light – or a laser, more specifically – with no halftone. This is done using red, green, and blue light (RGB).
Both printing technologies are suitable for photos (when it comes to giclée prints, Fine Art Prints – prints with very high resolution and as many colors as possible – are especially good for this.) For graphic works, and for text in particular, giclée prints are advantages because they can produce crisper edges on the text.