I don’t know what’s going on with you, but something is wrong. I downloaded and checked both of your pictures. Since I don’t have a Mac or Linux but a Windows computer, the Microsoft tool “File Checksum Integrity Verifier” was used. The file name is: fciv.exe, download and usage can be found HERE
I checked both of your images (file-a.jpg & file-b.jpg) here with both the MD5 and the SHA1 hash algorithms. Both images have the identical checksum.
//
// File Checksum Integrity Verifier version 2.05.
//
MD5
903494943b1ef3fbd56a387b5095366b file-a.jpg
903494943b1ef3fbd56a387b5095366b file-b.jpg
SHA-1
e7d378bfd8f726e64f14d80ddd43b0f2bf799845 file-a.jpg
e7d378bfd8f726e64f14d80ddd43b0f2bf799845 file-b.jpg
Then, as suggested by you, I created a test image in Photoshop and made a copy of it, for whatever reason.
myfile
myfilecopy
And checked both via fciv.exe. The checksums of the two images, like those of your images, are absolutely identical.
//
// File Checksum Integrity Verifier version 2.05.
//
MD5
f3f39f20ed16b47415fb9ef842093b5c myfile.jpg
f3f39f20ed16b47415fb9ef842093b5c myfilecopy.jpg
SHA-1
8802340420397e0da3ee6aa362296646d4d5246c myfile.jpg
8802340420397e0da3ee6aa362296646d4d5246c myfilecopy.jpg
Now I have sent both pictures to myself via email and checked them again. Needless to say that all checksums are identical.
//
// File Checksum Integrity Verifier version 2.05.
//
MD5
f3f39f20ed16b47415fb9ef842093b5c myfile.jpg
f3f39f20ed16b47415fb9ef842093b5c myfilecopy.jpg
f3f39f20ed16b47415fb9ef842093b5c myfile-email.jpg
f3f39f20ed16b47415fb9ef842093b5c myfilecopy-email.jpg
SHA-1
8802340420397e0da3ee6aa362296646d4d5246c myfile.jpg
8802340420397e0da3ee6aa362296646d4d5246c myfilecopy.jpg
8802340420397e0da3ee6aa362296646d4d5246c myfile-email.jpg
8802340420397e0da3ee6aa362296646d4d5246c myfilecopy-email.jpg
Conclusion:
At least in my network there seem to be no oddities. Everything is exactly as I expect it to be. For this reason, I can conclude that my Ethernet cable as well as my network transmit a bit-accurate signal.