Enternet=LAN is for locally, short distance connected devices.
DSL pertains to your home connection TO your ISP provider ( a phone company in the DSL case usually, the phone company provides tour Internet access). It requires a phone jack RJ-11 and is using your hone phone lines, so you can easily move it around. You must also install special filter on any land line phones in your home so your land line phones phones could work properly on the same wires.
LAN stands for Local Area Network, it allows multiple devices to connect to each other (via a router/switch or hub), but can it must connect to a WAN( Internet), via a ROUTER, which could translate and hide tour home(LAN) network from the Web/Internet. Usually the Router have integrted 4-port switch capability, which allows multiple LAN devices(wired or Wifi) to SHARE the same Internet connection(DSL / Cable / Fios, etc)
Example: you can have printers, laptops, gaming at home talking to each other via LAN(Enternet cables or Wifi), but can NOT connect to the Internet without some Internet Service provider AND a router. In the case of DSL usually the DSL modem provided by your phone/ISP company has integrated router+switch capabilities. DSL routers are usually useless if you move to FIOS or (cable company like Time Warner) Internet.