A wired Ethernet connection to your access point is advantageous because data can transmit back and forth simultaneously. It provides faster data transfer, a stable connection, enhanced speeds, and makes it more difficult for unauthorized users to intercept data. Setting up a wired connection for your access point can also be more time consuming. A wired connection makes your access point function as the WiFi base station or, if you use a mesh WiFi network, as the root access point.
A wireless connection to your extender and root access point can be less time consuming to set up, offers more WiFi access to dense locations, and can offer WiFi usage outdoors. Note that a wireless connection halves your bandwidth.
The WiFi base station or root access point, and WiFi repeater or extender access point, work together to cover a potentially large area with WiFi and this setup functions better to extend your network.