A network router typically connects two separate networks together and is responsible for routing the packets from one network to another. Advanced network routers can also control how the packets can be routed by using different routing protocols.
In homes and offices, you may use wired or wireless routers. They are used to connect the WAN side and LAN side together and routing the packets between the two networks. Wireless Routers are very popular today since they function as both a router and Wireless Access Point. In short, they convert the WiFi packets into Ethernet packets and also route these packets between the WAN and LAN networks.
WiFi Access Points are like wireless switches and connect devices within the same network. They are used for connecting WiFi enabled devices like laptops, smart phones, tablets, wireless printers to the network. The WiFi Access Point can be connected to a switch or a router. When connected to a switch, the wireless devices can communicate with the wired devices within the network. When connected to a router, the wireless devices can connect to another network like WAN.
Please note that WiFi Router can function as a WiFi Access Point but not vice versa.