I'm really not sure what you're trying to say. If you have an ethernet cable (is it really POE?), and you have wifi on the PC / laptop, that is saved with SSID credentials and set to auto-connect, it's possible in Windows (7, 10, at least, I think), to be connected to both wifi and ethernet at the same time. Note that Windows will try to "detect" the router (MAC address internally, and named externally), and sometimes it takes a while or doesn't detect due to some issue.
I'm really not sure what you're trying to detect or prove, here. It's just so much rambling.
When you say "connect to my router", do you mean, with ethernet, or wifi? Please be much more specific in your descriptions, and include pictures from all your tested cases.