Envy and Hate

If jealousy is the wanting of the beloved object, and envy is the feeling of competition with the rival, then I think jealousy is a normal emotion that shouldn't necessarily be considered negative. However, envy seems to be more about hatred of the rival. An envious person wont be happy if he/she gets the desired object/person/thing; he/she just wants to see the rival lose it and suffer. This sounds like hatred. I'm wondering why hate is not one of the seven deadly sins and envy is. Hatred is probably at the root at most envy, so how can hate and envy be distinguished?