What is the difference between a wireless bridge, an access point and a Wi-Fi extender?

An access point needs a cable. TP-Link describes access point mode as converting a wired connection into a wireless one. It works like a switch placed behind the router, so the Wi-Fi it creates has the full speed of the cable feeding it.

An extender or repeater has no cable. It receives the router's Wi-Fi and transmits it again, so every frame crosses the air twice, and Wikipedia's summary puts the throughput cost at 50% or more. TP-Link adds that extender coverage and speed fall off with distance from the router. An extender is the right tool for a dead spot inside the house. For a separate building it is weak, because by the time the signal reaches the far wall there is little left to rebroadcast.

"Bridge" means two different things. On many home routers, bridge mode is a setting that extends the existing Wi-Fi under a different network name, which in practice works like a repeater. A point-to-point bridge, the subject of this guide, is two directional radios aimed at each other that carry Ethernet between buildings. Neither radio serves phones or laptops. Plug an access point, a switch or a mesh node into the far radio, and the outbuilding gets its own full Wi-Fi network instead of a weak copy of the house's.