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?
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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Sentence 1 is correct if what is meant is to express past intent and further imply that it no longer represents present intent.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.