sake 的意思是“缘故/为了...的好处”,因此 For the sake of 表示目的,意思是“出于对…的缘故/为了…起见”.如：
She called on us merely for the sake of courtesy.她来访只是为了礼貌（的目的）.
We can't risk big things for the sake of small ones.我们不能因小失大（为了小事情的目的而冒险作大事情）.
result 的意思是“结果”,所以 As a result of 意思是“作为...的结果/由于…的结果”,表示的原因.如：
She died as a result of her injuries.她由于受伤（的原因）而死亡.
Her heart was slightly damaged as a result of her long illness.（由于）久病（的原因）使她的心脏受到一些损伤.
As a result of his pioneering work in the late 1930's,Earl Hines has been called the father of modern jazz piano.
本句的意思是赫因伯爵之所以一直被称作现代爵士琴之父是“由于他在20世纪30年代做出创举这一原因”而不是“为了他在20世纪30年代做出创举的这种目的”