About the progressive form(ie:My wife is flying to Madrid tomorrow)

[Nash2002]

In the grammatical lesson(progressive form), there are the articles:

"we want to describe an action that will be happening in the future "

if in that case, what's the difference between the following two sentences:

My wife is flying to Madrid tomorrow.

My wife will fly to Madrid tomorrow.

[Pechorin]

I've been taught the following:
The progressive tense, like in the example with the wife flying to Madrid, is used for a planned action. The woman has planned to fly to Madrid, she might have already bought a ticket, etc.

The future simple is sometimes used for a "on spot decision":

- We are on the bottom on everything, sugar, bread, butter. I'm going to the shop.
- Don't forget to buy some beer.
- OK, I will.

Well, I'm not sure how to qualify this example: if it's "on spot decision" or a promise, but in both cases the future simple is to be used.

[E2e4]

I think that "will form" doesn't go with adverb of time such as tomorrow, next month etc.

"OK, I will." is a perfect example.