Are hex editors called binary editors

This will print the offset and bytes in hex:

cmp -l file1.bin file2.bin | gawk '{printf "%08X %02X %02X\n", $1, strtonum(0$2), strtonum(0$3)}'

Or do $1-1 to have the first printed offset start at 0.

cmp -l file1.bin file2.bin | gawk '{printf "%08X %02X %02X\n", $1-1, strtonum(0$2), strtonum(0$3)}'

Unfortunately, strtonum() is specific to GAWK, so for other versions of awk—e.g., mawk—you will need to use an octal-to-decimal conversion function. For example,

cmp -l file1.bin file2.bin | mawk 'function oct2dec(oct,     dec) {for (i = 1; i <= length(oct); i++) {dec *= 8; dec += substr(oct, i, 1)}; return dec} {printf "%08X %02X %02X\n", $1, oct2dec($2), oct2dec($3)}'

Broken out for readability:

cmp -l file1.bin file2.bin |
    mawk 'function oct2dec(oct,    dec) {
              for (i = 1; i <= length(oct); i++) {
                  dec *= 8;
                  dec += substr(oct, i, 1)
              };
              return dec
          }
          {
              printf "%08X %02X %02X\n", $1, oct2dec($2), oct2dec($3)
          }'

These are different files.

From When is System32 not System32? [emphasis mine]:

In 32-bit Windows there is just one System32 folder which contains many native binaries (or hard links), and there is no way to execute 64-bit code on 32-bit Windows.

With 64-bit Windows, however, we have "Windows On Windows 64" (WOW64) which allows 32-bit processes to run through a wrapper, and there are some things to take into account in this scenario:

1. Only 32-bit DLLs can be loaded into 32-bit processes, and only 64-bit DLLs can be loaded into 64-bit processes.
   […]

2. 32-bit processes expect to work seamlessly on 64-bit Windows, so because of (1) we need to have both 32-bit and 64-bit versions of some binaries.
   […]

3. In order to facilitate (2) but not break native (x64) processes' behaviour, 32-bit processes get certain I/O redirected without their knowledge.
   […]

[…]

For 32-bit processes running on x64 Windows:
- %systemroot%\System32 is redirected to %systemroot%\SysWOW64
[…]

My guess is some hex editors are 32-bit and get redirected to SysWOW64, some are 64-bit and see the "real" System32. Different editors perceive different System32, hence different notepad.exe.

If you copy notepad.exe to a folder that is not affected and analyze the copy then all editors will show the same content. Which file will you see? This depends whether the copying tool is 32-bit or 64-bit.