They mean almost the same thing... Encourage means to give support, confidence of hope... Foster means to encourage the development of something... The difference is that foster is specific to development.

I agree with the other two answers, but I think it's worth adding that context can change the meaning (as always), and there's one very important example which is worth noting: To foster children = to take care of/be responsible for raising children It's not exactly the same as 'to adopt' which is permanent, but it has a very different from 'to encourage children' (which has the same meaning as the Italian 'incoraggiare').

Yes, exactly as Camille says. There’s a subtle difference. I encourage all my students to work hard to improve their English. In my classroom I try to foster a relaxed and friendly atmosphere. Hi to everybody in Italia and I hope your language learning is going well.