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$ cmp -s file1 file2

The above command doesn't return anything for the following cases:

• Case 1: both files (file1 and file2) are different;


• Case 2: both files (file1 and file2) are same.

I tried all the above cases, but my unix system is insensitive.

-s is for silent, it's to tell cmp not to output anything¹ but only to reflect whether the files are identical or not in its exit status so that it can be used for instance in an if shell statement:

if cmp -s file1 file2; then
 echo same
else
 echo differ or error
fi

Or:

cmp -s file1 file2 && rm file2

If you want it to output something, remove the -s. Then cmp will output a message when the files differ stating where they start to differ.

^{¹ except with some implementations for error messages when files can't be opened, not when they differ.}

I would question your case 1. If cmp doesn't return anything then the files likely are identical. Try diff file1 file and sum file1 file2 to confirm. Is it possible that the differences are in non-printable characters?