molahs:
The Ethernet board doesn't have pins at the bottom so I can't connect it to the UNO.
What you are saying sounds like utter madness but it seems that the real problem is that you don't know what you've got. The link does not display an Ethernet board, it is a Uno-based micro controller. The reason why you can't plug it into a Uno is because it is a Uno (somewhat disguised), hence no pins underneath.
Why do you need to connect an Arduino with Ethernet to a different Arduino? If all you wanted was an Ethernet shield, why did you buy the Arduino with Ethernet board?
Thanks to @Nick_Pyner & @PaulS. Indeed I don't know what I have.
Seems like the sales person in the shop was overly eager to help a newbie and sold me 2 uno boards instead of an Uno and an ethernet shield. Guess i'll be making a trip back to the store.
As a matter of interest, how would I program this ethernet Uno-based micro controller? Is it just like uno programming? Maybe it's worth my while to keep it, and have an extra uno. What puzzled me, was that it doesn't seem to have an atmega328 chip like the uno.