Why identical sticks are advertised with ECC and no ECC

I agree. The seller possibly mixed up ECC and registered properties.
Based on the pictures (and the description the eBay seller provides matches the pictures):

The "Non-ECC" is HMA82GR7AFR8N-UH and the other is "ECC" HMA82GU7AFR8N-UH. If those links are to be believed (which I think they are probably accurate) the first kit is actually Registered ECC and the second is Unbuffered ECC.