Internet access enables information gathering on the web.
Many "modems" (cable modems, DSL gateways or Optical Network Terminals (ONTs)) provide the additional functionality to host a LAN so most Internet access today is through a LAN such as that created by a WiFi router connected to a modem or a combo modem router, often a very small LAN with just one or two devices attached
Broadband Internet access, often shortened to just broadband, is simply defined as "Internet access that is always on, and faster than the traditional dial-up access" and so covers a wide range of technologies

