foster
to promote the growth or development of
to bring up (a child, etc); rear
e.g.
foster the thought of serving the people
树立为人民服务的思想
foster hopes for success
抱成功的希望

cultivate
to improve (the mind, body, etc) as by study, education, or labour
e.g.
cultivate a new generation
培育新一代
cultivate the habit of analysis
养成分析的习惯
cultivate a love of art

从具体可以看出，foster强调对儿童的抚养、供养；鼓励或促进事物的发展。
cultivate重点在于一种潜移默化、长期细心地育和培养

cultivate培养;陶冶,很多情况下培养的是抽象的东西.

例如---She cultivated her mind by reading.
她以阅读来修身养性。

foster
养育,抚养
We fostered the little girl while her mother was in hospital.
这小姑娘的母亲住院时,我们领养了她。

当然二者也经常可以互换的.界限不明显的.