てもらう and how it's used with particle に

Question

I was watching this video about てもらう and てくれる, and I don't really understand why てくれる always uses が, and てもらう always uses に to mark the person who does something for the speaker, especially about に and てもらう. For example, what's the difference between the following sentences?

さくらがパーティーに誘ってもらった

さくらにパーティーに誘ってもらった

why does てもらう always use に in the video? And not が？

Answer 1

もらう ("to receive") is a verb that can take up to three particles (i.e., trivalent). AがBにCをもらう means "A (gratefully) receives C from B".

彼女は母に指輪をもらった。
She received a ring from her mother.
_{(が is replaced to は because it's the topic of the sentence)}

が (or は) marks the subject who is the receiver, and に (or から) marks the giver. These rules won't change when もらう is used as a donatory subsidiary verb (i.e., when the given thing is a "favor" instead of a tangible object). Therefore:

さくらがパーティーに誘ってもらった。
Sakura was invited to a party (by someone, and she was grateful).
_{(Read this as though Sakura received an imaginary invitation.)}

さくらにパーティーに誘ってもらった。
[I/Someone] was invited to a party by Sakura (and I/he/she was grateful).

Of course you can use both が (は) and に and say something like this:

太郎が花子にパーティーに誘ってもらった。
Taro was invited to a party by Hanako (and Taro was grateful).

Answer 2

I remember when I first learned about してもらう、してあげる　and the like, it helped me to think translate it in my head as "to receive the action of ...~ing" or "to give the action of ...~ing" :

さくらがパーティーに誘ってもらった

Sakura received the action of being invited to the party.

i.e.; Sakura got invited to the party.

さくらにパーティーに誘ってもらった

[Someone] received the action of being invited to the party by Sakura.

i.e.; Sakura invited them to the party.