Im not sure what you mean by passphrase. If there are three sets of numbers then you (should) have three ways to connect. As you haven't given any specific info on this I would guess that One is for your Office (Wireless?), one LAN (EtherNet) connection (Not wireless) and one wireless for home ?

This could BTW also be eg. BlueTooth or some other infrared (Irda) connection.

You will have to find out more on your setups and post it here to get anymore concrete help. This is impossible to just guess. You will have to fill in the blanks.

It says what the networkcards name is above the info on each one of the connections.

And default gateway is the IP you would use to access your router