Covetousness would be the desire, the want, but envy would be the intense emotions that could accompany such a desire.
As to your middle 2 paragraphs, you've not contradicted what I said. Envy is (the intense emotions that can accompany) wanting what others have (outward focused, as you say) and jealousy is the (intense emotions that can accompany) concern that others will take what you have (inward focused, as you say).