My Windows 10 machine has an icon in the status bar which is linked to its network connectivity:
It can be either the one above (which suggests a Wi-Fi connection) or in the form of a "desktop", which suggests a wired connection.
At the same time I see the following default routes:
0.0.0.0 0.0.0.0 10.237.76.1 10.237.78.2 25 0.0.0.0 0.0.0.0 10.239.144.3 10.239.144.109 35
10.237.78.2 is the IP assigned to the wired interface and it has the smallest metric, which means that this route will be preferred.
This makes sense: when connect to a live wired network I want the traffic to go there.
In that case what does the logo mean?
Since I also see from time to time the "desktop" icon (when connected, like in the case above, to the wired network) I assume that this is a bug. So if the answer is "it is to have something but the logo does not matter as it is more or less random", I am fine with that answer.
Note: there is one usage which is useful and works correctly - the indication whether there is a connection at all and whether this connection reaches internet.