For example wikepedia says that
'pointing a web browser to the URLs http://127.0.0.1/ or http://localhost/ will access that computer's own web site'
Slightly inaccurate. It may do so. Equally well it may not bring up any website and it is even possible to display an different internal website from what you get when you use your x.x.x.x address.
127.0.0.1 points to your own machine, but that doesn't mean it will behave the same way once it reaches your machine
If you want a non-technical analogy, your can consider them different doors into your house.
There are both pointing to the same house but they are not the same thing.
It is possible for each door to take you into the same room or they could take you into a different room. It is also possible to lock one door and not the other.
When you configure a website, you specify which addresses to bind to and quite often the answer is all addresses. (That is equivalent to have all doors taking you into the one room)
You can also specify the website to bind to one address only. (That is equivalent to locking all doors except one.)
If you have two (or more) websites you can bind them to separate addresses. (That is equivalent to having each door going into separate rooms).
An example of how both references work, my Windows 7 computer has IIS installed, when I go into IIS Manager and right click on Default Web Site, it gives me a 'Edit Bindings' menu option. Selecting that bring up a list of bindings. I have only one, but for IP Address it has * which means IIS listens on all my ip addresses.