When talking about a wired connection, this generally means Ethernet via CAT cables, often CAT 5e or CAT 6 these days. While Ethernet is the more common wired connection in a residential situation, it is not the only one. Networking can also be done via coaxial cable, and this gets termed MoCA, which stands for the Multimedia over Coax Alliance (and no relation to the chocolate that gets put into coffee).
Yes, the coax wires that many users already have run in their home that traditionally got used for video applications can also be used for data transfers. There are many member companies that make up MoCA, including Broadcom, Comcast, Intel and Verizon.