Every piece of network hardware as a unique MAC address ("media access control address") which is assigned when the individual device is manufactured. The built-in hard-wired ethernet port will have its own MAC address and the WiFi dongle will have a different one of its own. If you buy a new WiFi dongle, it will have a different MAC address than the dongle your replace.
MAC addresses are expressed as six hexadecimal numbers. For example, 00-14-22-A1-23-FF or 00:14:22:A1:23:FF.
Your router assigns an IP address on your local area network to each MAC address which it finds. It can assign this IP address from a pool of available addresses ("dynamic IP") or you can force it to assign a specific IP address to a specific device's MAC address. See your router's instruction manual.
Because you will want whatever device you're using to control the web interface on your Brennan to be able to find your Brennan, you will want to make sure that your Brennan is assigned a static address so that it's always where you expect it to be on your local network.
You should be able to set a static address for your Brennan in your router. The B2 software will work automatically with an Ethernet connection and you do not need a WiFi password. (And, when you are using a hard-wired ethernet connection, you probably should remove the WiFi dongle which will free up a USB port for other use and avoid your Brennan having redundant network connections.)