Background

My wife and I take English classes provided by our companies, so we have different teachers. So now it happened that we had the same topic: future.

Both teachers are native English speakers, but I don't place too much faith on that. I'm a native German speaker but I couldn't teach anyone how the grammar of German future works.

The question

We (my wife and I but also our teachers) both agree that "will" and "going to" indicate something to happen in the future. We also agree that the difference is just a matter of probability. However, we have opposite understandings on that probability.

My wife / my wife"s teacher says:

"Probably", "maybe" and "perhaps" are keywords pointing towards to use of "will".

There are no keywords for "going to", but it should be used when something is very certain to happen.

I say / my teacher says:

"Going to" is used in cases with low probability

"Will" is used with high probability.

The latter model fits very well to what I have learned at school. However, my wife"s teacher says that one reason for Germans to have the difficulty is that we learn it wrong at school.

When to use "will" and when to use "going to"? Is it a matter of probability? Is it a matter of stylistics (e.g. will for the single sentence examples and be going to for the multi-sentence examples as pointed out in one of the comments)? Is it a matter of how far into the future (present prediction vs. future prediction)?

What I have tried

###Oxford Dictionary

I looked up the definition of "will (modal verb)" in the Oxford Advanced Learners Dictionary, sixth impression and it says:

1(a) (indicating future predictions)

1(b) (indicating present predictions)

2(a) (indicating willingness or unwillingness)

2(b) (indicating requests)

3 (giving an order)

4(a) (describing general truths)

4(b) (describing habits in the present or past)

5 (insistence on the part of the subject)

From these descriptions, my opinion is that "will" is used for higher probability (a general truth is more likely than something else, habits are more likely than non-habits). I also can't find any of the keywords in the examples given in the Oxford dictionary.

I also tried looking up "going to", but it's neither present under "going to" nor could I find it under "go".

###Inlingua textbook

Second, I looked it up in my English textbook, which is Inlingua English 2 Step 1. Unit 7 is about "Planning" and there is an exercise 7.3 about decisions. While I would consider a decision and plans as something with high probability (because I can influence it), all the sentences start with "going to", which contradicts my understanding. Unfortunately, the Inlingua book is quite crap, because it seldom gives definitions and bases everything on examples only.

Third, there is Unit 8 "Predictions" in the same textbook. Under 8.3 there is one of the rare cases of a definition:

We use "will" and "going to" to discuss forecasts that are quite certain.

This finally confuses me even more, since there is almost no difference any more.

###English Page

I also had a look at English Page / Simple future. It says

USE 1 "Will" to Express a Voluntary Action

USE 2 "Will" to Express a Promise

However, I don't see much of a difference between those in the examples. If someone says

I will translate the email, so Mr. Smith can read it.

is that a promise, a voluntary action or maybe both? I just don't get it.

The site also says

USE 3 "Be going to" to Express a Plan

It does not matter whether the plan is realistic or not.

If the plan is not realistic, that would be improbable.

Also, what is the difference between a plan ("going to") and a promise ("will")? What if I promise someone to follow the plan?

Is "I will travel to Switzerland" a plan (e.g. I have made a plan how to travel there), a promise (because I talk to my girlfried living in Switzerland) or a voluntary action (which it also is)? So use "will" or "going to" now?

USE 4 "Will" or "Be Going to" to Express a Prediction

Predictions are guesses about what might happen in the future.

Derived from "might", this sounds both suitable for improbable cases.