Any router that's repurposed as an AP, or a device that has an AP mode, needs to connect to a router - via CAT5 or a CAT5 replacement such as HomePlug/IP on powerline, or MoCA.
A WDS repeater, a.k.a. range extender, with its halving of throughput, uses WiFi to retransmit data to/from a router. Thus, a WDS repeater is in moment 1 a client device of the router and in moment 2, an access point for nearby clients.