Q: On Airport Express, under Wireless tab, what is the difference between join and extend?

Extend means you are using a wireless access point to extend the wireless range. This would usually be done using an Airport Express. Joining a network means you are simply connecting to the existing network. It is sometimes called "Bridge Mode." You can only Extend an Apple router with another Apple Airport device.

There is no such thing as Extending an Ethernet connection. So on an Airport Express you can connect wirelessly to an existing network and then connect an Ethernet device to the Ethernet port. The AEX becomes a wireless access point.

AirPort base stations- Setting up and configuring an extended wireless network (802.11n)

AirPort Express frequently asked questions (FAQ)