Both are pretty strong feelings in Spanish. Crimes have been committed for both, "envidia" and "celos".
When you want what the other person has, you use "envidia".
-Me da envidia que Juan se pueda ir de viaje y yo no.
I'm jealous that Juan can travel and I can't.
-No seas envidioso. Juan ahorró todo el año para irse y tú gastaste el dinero en ropa.
Don't be jealous. Juan saved his money the whole year so he could go on vacation and you spent all your money in clothes.
-Todos mis amigos me tienen envidia por ser el más inteligente.
All my friends are jealous that I'm the smartest.
-Mi madre me dijo que nunca envidie a nadie por lo que tiene.
My mother taught me never to be jealous of anyone for what they have.
-Hubieras visto a Lorena cómo se puso verde de envidia cuando vio mi vestido nuevo.
You should have seen Lorena how she was livid with envy when she saw my new dress.
When you think a person should love you and not someone else, you use "celos".
-No seas celosa. Pati sólo es mi amiga.
Don't be jealous. Pati is just a friend.
-Mi hijo mayor tiene celos de su hermanita, porque cree que la queremos más que a él.
My eldest son is jealous of his little sister, because he thinks we love her more than him.
-Roberto cree que me va a poner celosa si saluda a Carmen. A mí no me importa.
Roberto thinks I'll get jealous if he says hello to Carmen. I don't care.
-Resulta que ahora no puedo salir con mis amigas, porque mi novio se pone celoso.
So now I can't go out with my friends, because my boyfriend gets jealous.