Pasta is usually made with Durum wheat, also called semolina, it is a hard winter wheat with a lot of gluten which makes it the "hardest" wheat flour, this gives pasta its structure so it does not easily become mushy when cooked. Eggs come in only when making egg pasta like egg noodles, otherwise pasta is made with just Durum wheat, salt and water.
Bread is usually made with bread flour, this is second in the amount of gluten present. Gluten is needed because in bread it creates the structure, when bread is kneaded the gluten forms little strings that hold the bread together and allow the yeast to raise the bread. Without enough gluten bread would be flat and gummy.
Pie dough is usually made with pastry or cake flour, these flours have the least amount of gluten and the combination of "soft" pastry flour plus fat creates a tender and hopefully flaky pastry. If you make pie crust with bread flour it would come out very tough and chewy instead of tender.
Finally there is all purpose flour which comes out someplace in the middle of the amount of gluten present. All purpose flour does a fairly good job in most cases but it is a poor choice for pasta.