Flour can be divided into two categories. Flour from hard and soft wheat. Soft flour is far more common except in south where bread made from hard durum wheat is typical.
Farina di grano tenero (soft wheat)
Flour is graded as type 00, 0, 1, 2 and integrale. This grading refers to the ash content. Ash being the remainder when a sample of flour is burned. A flour with a higher ash has more minerals.
Farina di grano duro (hard wheat)
Semola di grano duro aka durum what comes in a few varieties.
Farina di grano duro, Integrale, semolato, and rimacinata.
Flour of Durum wheat
Semi wholemeal / brown durum
W, P and L
On a professional level it’s helpful to have an idea of how strong a flour is. The W value indicates this. This data comes from a test of the flour done using the alveograph machine. Flour with a high W value will have a high gluten content.
Info: (external sources)
Some of the finest flour producers: