To check if you are connected to either Ethernet or Wi-Fi, select Help, Diagnostics in the Navigation Drawer of the App.
If the Diagnositcs for the Player you have chosen displays a color coded signal strength indicator and a dBm reading, it is connected via wireless. If these do not show up, this Player is connected via Ethernet.
By default, if a network cable is attached to a BluOS Player, it will always attempt the wired connection first. BluOS Players cannot connect using both connections at the same time. A Player can only be connected as wireless OR wired.