Sentence 1:Simon said that he would come over next month.
Sentence 2:Simon said that he will come over next month.
Is these two sentences both correct?
If yes, How do I distinguish these two sentences?
The two sentences mean nearly the same thing, but with different nuances.
They are both examples of reported speech. In reported speech, we usually backshift verbs to show that they were spoken by someone else, that they're not our own words, and we're just reporting what that person said.
However, we also have the option of not backshifting the verbs. When we do this, we are saying that we think the words are true.
So, "Simon said that he would come over next month" is exactly the same as:
Simon said, "I will come over next month."
with no suggestion whether we believe it is true, just that he said it.
On the other hand, "Simon said that he will come over next month" means:
Simon is coming over next month. I know this because he said so.
The problem is that "will" has two major senses. One simply implies futurity. The other implies desire or intention. "Would" is simply the past form of "will."
Sentence 1 is correct if what is meant is to express past intent and further imply that it no longer represents present intent.
Simon said he would come over next month, but of course that will not happen after his car accident last week.
The use of "would" here implies that the intent to come next month no longer applies.
Simon said he will come over next month
implies that there is no reason to believe that intent has changed.
standard grammar for these:
Sentence 1:Simon said that he would come over next month.
Sentence 2:Simon said that he will come over next month.
would be these:
Sentence 1:Simon said that he would come over next month.
Sentence 2:Simon says that he will come over next month.
Only sentence 1 is correct. Let me explain:
Grammatically speaking, your question is about reported speech (reporting what someone has said inidrectly) and quoted speech (directing repeating the exact same sentence that the person has uttered).
The second sentence is wrong. In this case, only in quoted speech can we use "will". Therefore, the second sentence should be like this in order to be correct:
Simon said, "He will come over next month".
Here we are repeating the exact sentence that Simon has uttered.
The first sentence is correct. It is reported speech. In reported speech, if the first part of the sentence (He said that) is the past tense "will" turns into "would", because "would" is the past form of "will".
Simon said that he would come over next month.
Let me give you another example:
Quoted speech: He told me, "You will regret this." Reported speech: He told me that I would regret this.
For further information, read about reported and quoted speech.