Both are the honorific forms of "에게(or 한테)" and subject particles "이/가" repectively.^^/
Here are examples of them.
I wrote a letter to my mother.
= 나는 엄마+한테 편지를 썼다(not polite and intimate)
= 나는 어머님+께 편지를 썼다.(polite)
My mother wrote back to me.
= 엄마+가 답장을 보냈다.(not polite and intimate)
= 어머님+께서 답장을 보내셨다.(polite)
\^o^/