Ethernet is how computers connect to each other over a network. It is an older, very stable connection method.
USB (Universal Serial Bus) is newer and more traditionally used for connecting hardware such as printers, keyboards, mice, cameras, and so on. It can be less stable than ethernet but its advantage is that in the most basic of ADSL modems, you do not require a separate power cord.
Most people tend to recommend ethernet modems for connecting as it is less temperamental and easier to install, which makes connection troubleshooting much simpler. Ethernet modem/routers operate independently of your computer and functionality doesn't depend on which OS you run on your computer.
Google for "USB vs Ethernet modem" - you will find much information.