てくれる vs てもらう when the topic or subject is implied

Question

From my understanding てくれる and てもらう "mean the same" from the "receiver" point of view, but the way the topic and subject are placed is a bit different, for instance:

僕は友達にゲームのやり方を教えてもらった　and 友達は僕にゲームのやり方を教えてくれた　(I was taught by my friend how to play the game / My friend taught me how to play the game )

Now, my question is, When the topic is implied and therefore hidden, is it ok to use any of these?

(Talking to my friend) ゲームのやり方を教えてくれた　and ゲームのやり方を教えてもらった。

I got this question because latelly i've been hearing a lot of things like these

言ってもらって助かった

So is it ok to use both　（does the meaning change?), or should I stick to one? Or should I stick to the most common to set phrase in question?

Thanks in advance, and i'm sorry for any mistakes.

Edit: removed ありがとう from the sentence to avoid confusion and misleading from the main point of the question.

Answer 1

Personally, the difference is “Who made your friend teach how to play the game?” You? or your friend on his own initiative?

*ゲームするのを教えて sounds a bit funny, so I’ll modify it using やり方.

僕は友達にゲームのやり方を教えてもらった。

When I read this sentence, I had a picture in my mind that you had asked your friend to teach you how to play the game, and then he decided to do so.

友達は僕にゲームのやり方を教えてくれた。

sounds like your friend took in the situation where you needed his help and decided to teach you how to play the game. Whether or not you had asked him is not known.

The difference between もらう and くれる is the perspective you should see them from... もらう the receiver and くれる the giver.

(A)彼女に誕生日プレゼントを買ってもらったんだ！
(B)彼女が誕生日プレゼントを買ってくれたんだ！

Which sentence do you think you should use if it is followed by サプライズだったから、すごく嬉しかったんだよ。

The answer is (B), because it implies that she took the initiative in buying the present for you. (A) is saying that you made the first move to get her to buy you a present.

*広辞苑より
「もらう」自分のための行為、動作を他人に依頼し、させる意を表す。

Hope this helps.

Answer 2

The answer to the question is YES, you CAN! It can be replaced but please remember the subject is different. In the future when you modify the sentence, it's important to remember it.

• (彼は)ゲームするのを教えてくれた

• (私は)ゲームするのを教えてもらった

  • Good: 教えてくれてありがとう
  • Wrong: 教えてもらってありがとう

Reason: It can be two parts, "Thanks for" and "I received his teaching" or "He taught me". You can not say thanks for receiving myself in this case.

These are the differences between もらう and くれる.

• もらう to be given, receive, infected, awarded (私は病気/栄誉/本/給料をもらった )
• くれる let one have, give, do something for (Only from person to person. 彼は本をくれた, 彼は書いてくれた)

POINT: 彼は私に本をくれた He gave me a book = 私は彼に本をもらった I received a book from him

彼は私に書いてくれた = 私は彼に書いてもらった

くれた sounds a little politer or more formal than もらった.