It's tempting to look for certainty in grammar books, but it isn't there.1. We use the present continuous for what someone has arranged to do in the future.
2. We use "going to" for an intention, something we have already decided to do in the future.
The present continuous for the future and be going to have similar meanings.
The above context is quoted from some grammar books.
Just a small quibble. You've paraphrased from your understanding of a couple of grammar books. If you've quoted anything, you should have quotes around it, and an attribution.
Let's procede with the understanding that this is how you understood the entries in the grammar books, and how you've synthesised that understanding.
Question 1. If the above two tenses have similar meanings,
They aren't tenses; they're just constructions - ways of expressing something.
"I am visiting Sydney next week.", "I'm going to visit Sydney nexy week"
why do 'something we have arranged to do in the future and something we have already decided to do' have to be distinguished.
I can't see that they do have to be distinguished, in most cases. And your argument so far has been that the phrases mean the same.
One grammar book has used the term "'something we have arranged to do in the future" as an explanation for one use of the present continuous; and another has used the term "something we have already decided to do" as a use for the "going to" construction, and you are inferring that a distinction has been made.
But it is you who have made a distinction. Are you asking why you've made it?
Emma is seeing Luke tomorrow
Emma is going to see Luke tomorrow
If Emma said 'I will go to see Luke tomorrow (instant decision)' yesterday, how should I say if I tell my friend?
You can tell you friend that Emma said she would see Luke tomorrow. If you friend asks, "Are you sure?" you can repeat verbatim what Emma said, and perhaps together, knowing what you do about Emma, you will be able to come to a good guess about what is likely to happen.
If I learned from someone else that Emma would go to see Luke tomorrow,how can I know that she has arranged or decided?
You can't know what she's arranged or decided unless Emma has told her friend and her friend has told you. You know nothing at all except that someone told you Emma would see Luke tomorrow. To make any further inferences, you'd need to know which grammar books Emma and her friend use, and how seriously they believe in them. You'd need to know whether Emma uses phrases such as "I'm going to see Luke" without having made arrangements, etc.
No one at all takes these guidelines that seriously.
How should I say if I tell my friend?
You can only tell you friend what you know and what you've been told. You cannot tell your friend that Emma has made an arrangement, but no decision, or vice versa.
If I have planned to take my son to go to Disneyland in Japan in the coming Christmas but I have not bought the air tickets, does it mean that I have decided to take my son to go to Disneyland' not I have arranged to take my son to go to Disneyland..
To me, if you had brought the tickets, your arrangements would be slightly more advanced than if you hadn't. However, it would be totally misrepresenting the purposes of a grammar book to then say that you should move slightly toward a preference for using the present continuous. You do not have to change from "I'm going to take my son to Disneyland" to "I'm taking my son to Disneyland" after you've bought your tickets.
Hence, I say ' I'm going to take my son to go to Disneyland in Japan in the coming Christmas ' not ' I'm taking my son to go to Disneyland in Japan in the coming Christmas '
Would be appreciated for your help.
What you have read are guidelines about how these constructions are usually used. They are not definitions.
The difference between these two constructions is barely worth the time we have both spent on it. I'd suggest you choose your favourite form and use it all the time until a natural difference occurs to you. If it doesn't, then it won't matter.
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