What is the difference between 「もらいませんか」 and 「もらいましょうか」? [duplicate]

Question

I came across this fill-in-the-blanks question in a reviewer:

にもつ、＿＿＿＿＿　か。

The choices are もらいません or もらいましょう.

My current understanding is that もらいませんか is of the form V-ませんか which translates to "why don't we/I V?", while もらいましょう is of the form V-ましょうか which translates to "shall we/I V?".

If I use もらいません, then it would mean "Why don't I receive your/that luggage?".
If I use もらいましょう, then it would mean "Shall I receive your/that luggage?".

The correct answer was もらいましょう.

But don't they both mean the same thing?
What is the difference between the two and when to prefer one over the other?

Answer 1

I guess ～ませんか and ～ましょうか are sometimes taught as being two similar ways to make a polite suggestion.

Indeed, they can be used with a somewhat similar meaning, for example in

行きませんか vs 行きましょうか

when the context suggests

why don't we go (together)? / would you like to go (together)? / shall we go (together)?

In fact, the two constructions actually mean something completely different:

• V + ～ませんか is asking (politely) if the other person might want to do V

• V + ～ましょうか is offering (politely) that you do V.

Indeed, the context could suggest translating

行きませんか
why don't you go (without me)?

行きましょうか
shall I go (instead of you)?

Of course, for your example, ～ましょうか should be the natural choice:

にもつ、もらいましょうか
shall I take the luggage?

にもつ、もらいませんか
why don't you take the luggage?

Answer 2

I like Earthjin's answer so I thought about leaving this as a comment, but it was too long so I'll post as an answer. Think of it as supplementary content.

「V + ませんか」can be translated in different ways depending on the context, but the easiest way is to deal with it is to think of it as "Won't you V?" or "Would you V?".

「夕飯行きませんか？」→ Won't you go to dinner (with me)?

「やめてくださいませんか？」→ Would you please stop (that)?

One notable exception to this rule is when you see 「~ 思いませんか？」. Even though it looks like a 「V + ませんか」form, the meaning can mean "Don't you think ~~?", depending on what comes before that phrase. This won't be confusing once you get more familiar with what comes before (or you may already be at that level of proficiency), but for beginners this could be a bit confusing at first.

「V + ましょうか」on the other hand is always either "Shall I + V?" or "Shall we + V?", always involving and never excluding the speaker.

Answer 3

にもつ もらいませんか means "Why don't you receive the luggage?". So, it doesn't work in this situation.

(Incidentally, I'm kind of surprised that you don't seem to wonder about にもつ being unmarked with particles because that's an advanced grammar that's not taught in any translated educational materials as far as I see.)