Yup, there are two different kinds of 'address' that a computer has.
One is the hardware address (MAC address, or as Apple calls them 'Ethernet ID' or 'AirPort ID') which is essentially the (supposedly) unique serial number of the networking HARDWARE. All hardware addresses are composed of six sets of 8-bit hexadecimal values usually stated as xx:xx:xx:xx:xx:xx, where each set of 'xx' is a pair of characters, 0-9 and a-f in each digit. Apple's AirPort hardware all starts with 00:14:51:xx:xx:xx, and Apple's Ethernet hardware all starts with 00:16:cb:xx:xx:xx. (For current hardware.)
The other is the software address (IP address, or Internet Protocol address,) which is assigned by the server you are connected to. There are two versions of Internet Protocol. The older, MUCH more common IPv4 (Internet Protocol version 4,) which is four sets of 8-bit values in decimal usually stated as xxx.xxx.xxx.xxx; and the newer, not-yet-in-widespread-use IPv6 (Internet Protocol version 6,) which is eight sets of 16-bit values in hexadecimal, usually stated as xxxx.xxxx.xxxx.xxxx.xxxx.xxxx.xxxx.xxxx. They two can be converted by using a certain algorithm. So, for example, on the network I'm currently on, I have an IPv4 address of 192.168.199.110 and an IPv6 address of fe80:0000:0000:0000:0214:51ff:feed:2c87. If you do the conversion, you will find that the IPv4 address is encoded entirely in the last two groups. (Sorry, I don't know the conversion algorithm off the top of my head.)