What is the difference between iron deficiency and iron deficiency anemia?

Matter of degree: When iron intake is inadequate for a prolonged period, iron storage in body is depleted. This is called iron deficient state. When this iron deficient state continues and iron store is further depleted, anemia develops, namely iron deficiency anemia.

Iron deficiency: Iron deficiency is the lack of iron in the body. When the level of iron is so low that hemoglobin cannot be produced, then you develop anemia: iron deficiency anemia. This is the simplified explanation.