"Ethernet" is a term that many users use to refer to devices within a small, "local" network, which are usually connected via category 5, or "Ethernet" cables. "Internet" generally refers to a connection to the world wide web. For instance; you do not refer to a network cable as an "internet" cable. The term "ethernet" helps to clarify the means of connection to the web, or to a network.(e.g., USB, wireless, phone line/modem, ethernet, serial cable, etc.)
Hassam has has further explained what ethernet is above. In the past, most internet connections were made via modem over phone lines. Broadband connections simply connect to an ISP in much the same way as networked "local" machines connect to each other.