Will or going to ...

I was having lunch with my English teacher today. He asked me : "what are you going to do after lunch". I replied : "I'll go to do some shopping". He told me that I had to use 'going to...' as I had planned to go shopping and say : "I'm going to do some shopping".
Any clues for not confusing these two futures ?

I hope this helps. I extracted it from my own class notes.
Use __ when:

WILL
1. definite future
2. Snap decision
3. Determination to do something
4. A request (interrogative)

I think we use "will" for a spontaeous decision and "going to " for a decision you've already made. A good example is when someone calls you and you want to note something down, you say : "I'll take a pen" and not I'm going to take a pen. Another example is when you are ordering your food in a restaurant. You say to the waiter : "I'll take scallops with baked potatoes."
You say "I'm going to canada this Summer ." because you have planned your holidays.
Natives be able to tell you more.

Sorry, here it continues:

5. A willingness or offer to do something
6. A promise
7. An inability or refusal to do something (will not)

GOING TO

1. Intention or Decisions
2. Strong probability based on evidence

PRESENT SIMPLE

1. Future event on a timetable (e.g. The University term begins on October)

PRESENT CONTINUOUS

1. Definite Future or arrangement (We are meeting the teacher tomorrow)

For further details, just ask me. Any doubts or requests for examples, I've got a lot...

However, I can't be 100% sure about this; but that is what the teacher told me.

Wow, that all sounds so complicated! To me, "I'll do some shopping" or "I'm going to do some shopping" are both perfectly correct in that situation. "I'll go to do some shopping" is OK, but maybe too complex--it sounds like you tried to use both methods in one sentence ;)

I don't understand David's list. I think I would have to see examples for each of those to know what is meant by them.

I'm a native speaker--so I didn't learn it by those rules! But the way I think of it is:

Use going to for the immediate future, something you are about to do in a minute, an hour, right after lunch, etc. It could mean later in the future if you specifically say so, as in "One day I'm going to travel around the world"

Will is just general purpose future tense. It signifies that you definitely intend to do something.

And in the example "I'm going to Canada this summer" the term "going to" is being used in its other meaning, that of physical movement. To use it in the sense of this discussion, you would say "I'm going to go to Canada this summer"

Wow, I prefer your explanation Lana! It's much simpler to get across. (Sorry David Bosh ;) but thank you anyway)

Mine is not an explanation, it's just a list of circumstances when to use going to, will, etc.

So it means that 'going to' is used when intending to do something, or going to do something in a determined time; and 'will' for saying that you'll do something someday, or something that will definitely happen(e.g. My brother will be 16 next year). That's what I took in from Lana's, or... Am I wrong?

By the way, it's Bosch. lol

Sorry typo!
spontaneous

David Bosch, thank you for your explanations.
That would be nice if you could make examples of each case (circumstances). It's easier to learn.
David do you study English as a second language ?

Thanks Lana
I confuse these two too.
The explanation of Chantal is somehow easy to understand for me but maybe not complete.

I think your teacher was being overly picky. If I'd asked my friend "What are you going to do after lunch?" and (s)he replied "I'll go to do some shopping", I'd think nothing of it.

I think David, Lana and Chantal pretty much covered it but I don't agree that "going to" is only for the immediate future (unless specified). I don't think that there is anything wrong with "The sun is going to expand, then burn out and collapse."

Niki: Yes, well, in fact I study it as a third language after german (native) and spanish.

Let's see, some examples given to me were:

1.1 My brother will be 16 next year.
1.2 OK, I'll go to the cinema.
1.3 (I wrote it so fast that I can't understand it, sorry)
1.4 Will you help me?
1.5 I will help you with your luggage.
1.6 Thank you, I will give it back to you in a week.
1.7 This bulb won't light.

2.1 I'm going to study Electronics next year.
2.2 It's going to rain today.

3.1 The College term begins in October.

4.1 We are arranging an excursion to St. Ive's.

Hope this helps, and I repeat, this are only my notes of 8th grade in secondary school.