High gluten flour and bread flour is produced from hard wheat. High gluten flour has a gluten percentage of about 12-14% while bread flour contains about 10-13% gluten. Both flours are almost completely made of hard wheat, but some high gluten flours are treated to reduce starch content, raising the gluten content to around 14%. These flours are generally used for making breads. High gluten flour is reserved for breads that are extra elastic such as bagels and pizza.
Cake flour is produced from soft wheat and is low in gluten content (8-10%). This flour is used for making delicate cakes. Baked goods made with cake flour has a tendency to crumble because of the low gluten content.
All purpose flour is made from a mixture of hard and soft wheats. The gluten content ranges from 9-12%. This is the most versatile flour because it can be used to make both cakes and breads. However, breads won't be as chewy and cakes won't be as tender as if you used bread or cake flour.
Pastry flour is also a mix of hard and soft wheat flours with an emphasis on soft. Generally, the gluten content is 9-10% and is often recommended for pie crusts.