In order to connect to anything over a network each device needs a unique IP address, normally provided by a DHCP server (typically found on a router). When you plug your laptop directly into the Teranex Mini, your laptop first tries to send a request to get an IP address for itself, however the only other device on that cable is the Teranex, so your laptop does not get one. Similary when you plug the Teranex mini into the network it requests an IP address for itself, but the only other device on the network is your laptop, which is (normally) not running a DHCP server program and the Teranex does not get one.
On top of that, because your laptop is connected to WiFi, its wireless interface DOES have an IP address, and because the wired interface does not, will only try to communicate over the wireless interface, which is not connected to the Teranex. However, if you turn your wireless interface off, then the laptop will fall back to only using the wired interface where it will eventually see the Teranex.
You need to plug the Teranex into your router, (or a network switch connected to a router), let it get an IP address, and then you should be able to communicate with it over wireless. Or if you ALSO plug a wire from your laptop into the same router (or network switch connected to your router) it will get an IP address and be able to communicate with the Teranex.