One is giving, the other is receiving. And both can be confusing.
First off, these are which verb means what, and where to use them:
あげる (subject gives to someone outside your circle)(receiver is labelled with に)
Humble form: 差し上げる {さしあげる}
.
くれる (subject gives to someone in your circle)(receiver is labelled with に)
Honorific form: 下さる {くださる}
.
もらう (subject receives)(giver is labelled with に)
Humble form: いただく
.
When a sentence has a が and に it becomes a bit clearer as to the difference. But, to make it hard for us Japanese learners, these often get dropped, because they are obvious to the speaker and listener.
Even though give and receive might seem to be opposites, it is possible to ask for something using either.
もう少し説明していただいていいですか？Would it be okay if I receive a little bit more of an explanation.
(The above puts focus on the receiver)
この問題を説明してくれますか？ Could you give me an explanation to this problem.
(The above puts focus on the giver)
