LAN and Wifi are two separate things. LAN is a local area network which includes all devices: (computers, mobile phones, printers etc) connected over Wifi or cable inside your local network.
Wifi is a type of connection for connecting your devices inside your local network devices.
As far as your question is which connection is better cable connection or wifi connection.
Every connection has own benefits the cable connection is mostly more reliable than a Wifi connection. But when you are using WIFI connection you don’t need extra cables to use the Internet. But keep in mind for WIFI connection you will need extra devices such as WIFI router and if you are using PC you will probably need WIFI USB adapters (check in our article) so that your PC can connect to the internet. On another side, you will need cable for connecting your network device and router from your ISP. The Ethernet cable can cost you money so you must calculate what is cheaper for you using standard cable connection or Wifi.