Does an Access Point Need to Be Wired to the Router?
An Access Point is wired to the network, whereas connectivity points that are meant to extend the network range are connected to the network via WiFi, and are called extenders or repeaters. If you wish to expand your home network, you do not need the extender wired to the router.
And a router can function as an AP, but an AP is not necessarily a router -- I will explain.