Version same for both devices: Avast 2015 (10.3.2225)
I noticed that the system had identified them differently. One as Current device online, and the Other device as Unknown. Online device OS Windows 7 32-bit. Unknown device OS Windows 10.
That told me the whole story! Earlier, I had upgraded from Windows 8.1 x64 to Windows 10 x64. I wasn't quite happy with the way a few critical applications went along with Windows 10 x64. Therefore, I formatted the C: drive, and made a clean install of Windows 7 Home Basic x86. On both occasions, the System had asked me to activate my license. This could be the reason why I found two devices with same name. One showed up as current device, and the other as Unknown device.
Original post was submitted based on what had showed up on one screen. This post is being submitted based on what shows up on another screen. It came to my notice on probing further, primarily encouraged by your reply to my original post. Thank you, David!