Some notes on wheat with relevance to breadmaking and pasta
Harold McGee's On Food and Cooking, the best food reference there is (at least in English), has a lot of good detail about this, including the latin names of the various species and varieties of wheat.  Below are some common wheats and related grains:

Wheat Berries: http://www.flickr.com/photos/debunix/247497350/
(larger versions available on flickr, http://www.flickr.com/photos/debunix/247497350/)

Clockwise from Top:
Rye (Cecale cereale)-greener than wheat, and more variably colored in general
Barley (Hordeum vulgare)--partly pearled berries are pale here
Kamut (Triticum turgidum)--unusually long, thin, otherwise more resembling durum
Durum wheat (Triticum turgidum diococcum)--longer, thinner, more translucent and golden than T. aestivum
Hard white wheat (Triticum aestivum)--compact, light colored, more translucent than soft white
Soft white wheat (Triticum aestivum)--plump pale kernels
Oats (Avena sativa)--pale, narrow, softer kernels
Spelt (Triticum aestivum spelta)--redder, plump, often has hulls still attached

Not pictured: hard red and soft red wheats, which look like hard red and white wheats except they're the same color as the spelt here.

Modern bread wheat, T. aestivum, has a variable protein content from 10-16%.  The lower protein content versions are called soft, and the higher protein wheats are hard.  Their protein forms a highly elastic and strong gluten when wetted and kneaded that is good for breads.  The higher gluten content of hard wheat makes for breads capable of rising higher.  The soft wheats are used for pastries, cookies, and cakes, where too much gluten makes for chewinesss rather than crispness or softness.  When milled into flours, the protein content is lower than that of the whole wheat berry because protein is lost when the bran and germ are sifted out to make white flour.

American white all-purpose flour is a mix of hard and soft wheats, with a mid-range protein content (11-12%), that makes ok bread and ok pastries.  Pastry flour is lower protein (8-9%), and specialty bread flour is higher (12-14%).  European bread flours are noted for having lower protein content than American flours, because they don't have the same access to very high-protein spring wheats grown in the northern great plains and Canada. You'll find specialty "European", "French" or "Italian" bread flours mixed to 9-10% protein to approximate these different flours.  The combination of different protein and varied degrees of hydration (percentage of water in the recipe) are what give many French and Italian breads their big soft holey crumbs, and makes for good pizza dough.  Cake flour has lower portein content still at 7-8% (I think sometimes extra starch is added to cut the percentage of protein).

Durum and Kamut are both older types of wheat than modern T. aestivum bread wheats, with a different proportions and types of gluten than bread wheats.  Their gluten is very strong, but not as elastic, so doesn't stretch as well to accomodate pockets of gas from growing yeast.  It works very well to hold together pasta, however.  Durum is the source of durum flour and semolina (a coarser variety of flour from the same durum berry).  Durum flour is more golden and makes breads with a warm, golden crumb, and a slightly nuttier flavor than bread wheat.  I like to use 20-50% durum sometimes for breads, especially in flatbreads where the degree of rising is less critical, to take advantage of that flavor.

Spelt is a very old variety of wheat, neither a modern bread wheat, nor a durum wheat, and though it looks much like it, it is not the same as emmer or farro.  It has a high protein content (16%) but the gluten is not very elastic, and will not make a bread as light as a modern bread wheat of the same percentage of protein.  I particularly like to use it in soups, although probably any wheat would do as well.

As used here, white flour (sifted or milled to remove the bran and germ, for better shelf life and maximum rise in breads) is not to be confused with white wheat or red wheat; these refer to the color of the bran of the wheat berry, and the color is independent of the protein content or hardness of the wheat.  Red wheat bran tends to be a bit more bitter tasting than white wheat brans, and may be part of what puts some people off when they taste whole wheat baked goods.  Durum and Kamut also lack that bitter edge.

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