What is the difference between the modem and a router?

Hi,
The modem and the router are just the same, but the router has its antenna and the modem doesn't. Can anyone tell me the difference between these two ? Do the modem and router have the same concept, like configuring it?
I also wonder why a modem has RG11 and a Router has RG45. What are all these? What is the advantage of it in computers, laptops, notebooks, iPhones etc.?
Thank you.
