How many different types of anemia are there?

Many. There are many types. Anemia means that there is a decrease in the number of red blood cells. Probably the most common type relates to bleeding, e.g., from menstrual periods, rectal bleeding, trauma, etc. Another cause is hemolytic - where red cells are destroyed. Another can be bone marrow dysfunction, where not enough red cells are produced. Another is dietary (b12 or iron deficiency).
Many anemia causes. Anemia simply means a red cell mass outside normative values for age/sex. There are many causes, both acquired (eg., fe or folate (folic acid) deficiency, marrow infiltration, etc.) and constitutional (eg., hemoglobin disorders, red cell membrane disorders, enzymopathies, etc.). Fe. Deficiency is overwhelmingly the most common cause of anemia in the us. Your doctor can help sort out possible causes.