If you can think of any cutting styles I've missed, please comment below so I can add them. Thanks!

Cut Style	Explanation
Slice	Broadly refers to cutting produce into shapes such as strips, wedges or discs. Usually recipes include a more detailed explanation.
Chop	Chopping usually refers to cutting produce into uniformly smaller pieces (with a knife).
Dice	A variety of chopping, diced pieces of fruit or vegetables are typically 1/8 to 1/4 inch cubes. This is usually done by slicing the produce and then cutting across the sliced sections to make roughly square pieces.
Mince	Another variety of chopping, minced produce is cut into very small pieces (smaller than diced pieces). Produce can be minced in a food processor or with a knife, by slicing thinly, then chopping back and forth until the food is the desired size.
Julienne	Also called "matchstick," this way of cutting is often achieved with a mandolin slicer with julienne blades. Produce should be sliced into long, thin pieces (like matchsticks!).
Spiralize	Using a "Saladacco," "Spiralizer" or mandolin attachment, you can cut produce into long, curly strips (I once made a spiralized section of beet that was six feet long!). This type of cut is the most common in preparing veggie (zucchini) pasta, but also works great with carrots, beets, and other dense vegetables.
Chiffonade	Most often applied to leafy greens and herbs, chiffonade means to cut into delicate strips. This is frequently done by stacking and rolling the greens, then slicing perpendicular to the roll.
Peel	Often recipes call for the tough or irregular skins of fruits or vegetables to be removed by peeling them. Most produce can be peeled with a "peeler" (specially designed for peeling, also known as a potato peeler) or a paring knife. A peeler can also be used to make vegetable ribbons.
Ribbons	By peeling a vegetable in a long strip down to its core, you can achieve vegetable ribbons. Rotating the vegetable while you peel around its body (rather than straight down the side) produces long ribbons that can substitute for spiralizing if you do not have the extra tools.
Shred	Produce is easily shredded with a grater. Since graters often have different thicknesses, the recipe should specify small or large. If you need to make a judgement call, keep in mind that smaller pieces often have a sweeter taste.
Zest	Usually recipes call for the zest of citrus fruits, which is the colorful, outer part of the peel. Also assumed in the word "zest" is very small pieces. Zesting tools obviously work the best, but you can achieve the same result with a small grater or by slicing shallowly into the peel in a checkered pattern, and then peeling the zest off thinly with a paring knife.

Source: Living Cuisine: The Art and Spirit of Raw Foods" by Renee Loux Underkoffler