「もらえませんか？」と「くれない？」
I am watching a Japanese drama and realize that (other than the fact when 敬語 is used i.e. いただけませんか) characters use either ～てもらえませんか or ～てくれない when making requests. According to what I learnt, もらえませんか is more polite than くれない? And the subject of もらえませんか is the receiver of the action while subject of くれない is the initiator of the action? Other than that, are there any other differences as it seems to me they are used interchangeably.

Question

Answer

～ていただけませんか。
～てくださいませんか。
～てもらえませんか。
～てもらえない？
～てくれない？
～てもらえる？
～てくれる？
～て。

Basically these are all different variations of ～てください, to make a request. And as you know, ～ていただけませんか is the most polite and humble while ～て。is the most casual. So, you're right; もらえませんかis more polite than くれない？

The subject and receiver is usually not mentioned because it's obvious. Actually I recommend that you don't think about that too much because it makes the grammar complicated. Anyway here is my explanation.

Let's say you are asking the teacher or your friend to correct your email.

「（私は先生に）このemailを直してもらえませんか？」
The one who corrects the email is 先生.　=agent of 直す
The one who has the email corrected is 私。=subject and receiver of 直してもらう

「（あなたは）このemailを直してくれない？」
The one who corrects the email is あなた.　=subject of 直してくれる。 
The one who has the email corrected is 私. =receiver of 直してくれる, but not the subject of the sentence itself.