Hemoglobin is made of two matched globins, alpha and beta. Each person has two beta globin genes. There are many different mutations or deletions of the beta globin gene, including beta thal, HbE, HbS and Lepore. Hemoglobin E is normally a functioning hemoglobin, but when one globin gene is HbE and the other is beta thal, then a moderate to serious thalassemia will occur. Some of the possibilities are HbE carrier, which is one normal beta globin gene and one defective beta globin gene, HbEE, where both genes are HbE and is normally a condition with no symptoms and HbE beta thalassemia. These are all defects of the same gene. If one has HbE trait, about 33% of their adult hemoglobin (HbA) will be hemoglobin E. If one has co-existing alpha trait, the hemoglobin E percent will be under 30%. One who has HbEE will produce mostly hemoglobin E. It is only when HbE and beta thal are found together that problems arise.
Alpha globin is produced by 4 alpha globin genes. These are on a separate chromosome from the beta gene. All defects of this gene result in less alpha globin being produced. If alpha thal trait is present in beta thalassemia or HbE Beta thalassemia, the overall condition is often moderated, and not as severe because less alpha globin is produced, which matches better with beta thalassemia because there are fewer excess alpha globin chains.
So HbE is always a defect of the beta globin gene, just as beta thal is always a defect of this same beta globin gene, and not a defect of the alpha gene.