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Hello, everyone. I saw the following pairs of sentences in Practical English Usage #221.6.(Mine is the oldest edition) The book doesn't explain much about their differences, so I post them here to see if someone could tell me what their differences are. Please help me, thank you very much!!

What will you do next year? / What are you going to do next year?

All the family will be there. / All the family are going to be there.

If your mother comes, you'll have to help with the cooking. / If your mother comes, you're going to have to help with the cooking.

You won't believe this. / You' re not going to believe this.

Next year will be different. / Next year is going to be different.
Comments  
Which is the subject of that section? Write its title.
Marius HancuWhich is the subject of that section? Write its title.

It's future(3):will/shall (information and prediction).
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Well, in effect the title for the section from which you seem to have picked up all your examples is:
future(3):will/shall (information and prediction)
6 shall/will and present tenses: both used
Swan says there:
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Often shall/will and present/time forms (especially the going to structure) are possible with similar meanings.
The choice depends on whether you want to emphasize present ideas like intention/certainty ([use] present tenses) or not ([use] shall/will).
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This, to me, says everything. You just have to think about it and understand it.
And next time when you post, do not say the book doesn't say enough, because to me he says exactly what is needed. And you should have posted what he says, too, like I did in the above. Do not speak badly about good books.
Marius Hancu The choice depends on whether you want to emphasize present ideas like intention/certainty ([use] present tenses) or not ([use] shall/will).

This is the part I don't understand. Does the book mean that Next year is going to be different. is more certain than Next year will be different.?

And All the family are going to be there. emphasizes the fact that "all the family "want" to be there", whereas All the family will be there. does not shows their intention to come, and is just making a prediction?

In my opinion, "will" can mean "intention" (according to what I found in the Longman Dictionary of Contemporary English http://pewebdic2.cw.idm.fr / :used to show that someone is willing or ready to do something: Dr Weir will see you now.), if that is the case, then could All the family will be there. and All the family are going to be there. mean the same?

The reason I didn't post what it says in the book is that I was thinking that since I'm a non-native speaker, I couldn't tell what the difference is, but a native speaker might have a clue, and I think a native speaker would tell the difference without the help of the grammar books because they use English a lot more than I do. So I didn't post the words in my book.
Marius Hancu Do not speak badly about good books.
Well...any "good books" could have its insufficiencies (Think why PEU has so many editions so far). I'm not saying that PEU is not good, in fact, it is one of the best grammar books I've ever read. I've read many grammar books so far, and I realized that it's impossible to find a "perfect" grammar book. But PEU is close to it.
Viceidol What will you do next year? / What are you going to do next year?

All the family will be there. / All the family are going to be there.

If your mother comes, you'll have to help with the cooking. / If your mother comes, you're going to have to help with the cooking.

You won't believe this. / You' re not going to believe this.

Next year will be different. / Next year is going to be different.

To me, there is no discernible difference in meaning between these sentences.

However, the "going to" forms are, to varying degrees, more conversational.

Other people's usage may differ

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The choice depends on whether you want to emphasize PRESENT ideas like intention/certainty ([use] present tenses) or NOT ([use] shall/will).
This means that you can use both, depending on the stress you want to make:

When you want to stress/accentuate your current/present plans/intentions/certainties about the future, use going to.
When you not want to stress those current/present plans/intentions/certainties about the future, use will.