So, it is quite possible that those who have carefully studied the subject and come to the conclusion that the two terms are identical in their usage are correct.
Yes.
There are several possibilities here. The term "kingdom of heaven," occurs 32 times in scripture, all of them in Matthew. It could be a coincidence, perhaps an issue with the translation. Was it put there by God or by men?
A careful study of the terms in question here, will not be sufficient to make a conclusion. I submit that my conclusion and your conclusion will in part, be based on what we expect to find.
I believe that there are no idol words in scripture. Whatever we find in scripture was put there by God and is profitable doctrine, reproof, correction, and instruction in righteousness. God does not deal in coincidence. God requires that we labor for that meat which endureth unto everlasting life and God increases our understanding according to our diligence. God requires that we prove all things and he has given us the means to do so.
Something like the term "kingdom of heaven" used 32 times in Matthew and nowhere else in scripture, is a characteristic found in all scripture.