there is a discrepancy in platform.machine() behaviour on mac ARM:

In python2.7.16 ,  platform.machine() returns : "arm64"
In python3.7.9 , platform.machine() returns : "x86_64"

How did you install python3.7?

Platform.machine() will return "x86_64" when running in Rosetta 3. That is, when python itself is an x86_64 binary.

I downloaded it from : 
www.python.org/ftp/python/3.7.9/python-3.7.9-macosx10.9.pkg

That installer contains intel (x86_64) binaries. The behaviour of platform.machine() and platform.processor() is expected, due to Rosetta the binary runs as if it is running on an Intel Mac.

There is a "universal2" installer for Python 3.9.1 which will run natively on Arm systems.  The experience with 3th-party packages ("pip install ...") might be a bit rough though: this installer variant is quite new and I expect that most packages with C extensions do not yet have binary wheels for this variant.

Note also that Python 3.7 is now in the security-fix-only phase of its lifecycle meaning it no longer receives non-security bug fixes and binary installers for it will no longer be produced.  In particular, Pygthon 3.7 has not been updated for macOS 11 and Apple Silicon Macs and, as Ronald notes, it will run on Apple Silicon Macs using Rosetta 2 translation, there are some things that do not work correctly on Big Sur, like find_library functions.  If at all possible, you should upgrade to Python 3.9.1 which is supported on macOS 11 Big Sur.