What is the difference between an Access Point and a Wireless Router ?
An Access Point is a radio transmitter/receiver that is most widely used to bridge wireless and a wired (ethernet) network. An access point only provides an interface/portal for wireless clients to connect to your existing LAN. It does not route traffic between different networks, rather provides wireless access to an already existing local wired network.
A Router has additional functions: It allows multiple clients to connect to the Internet by serving internal IP addresses, has NAT (Network Address Translation) capabilities, often a built-in switch as well. It 'routes' traffic between two different networks, usually the Internet on the WAN side, and your local area network on the LAN side.
The most common purpose of a NAT router is to connect multiple computers to the internet (using a single external IP address provided by your ISP). It routes data to/from the multiple clients on the LAN side, appearing as a single device on the WAN/internet side. An added feature to this NAT setup is that client PCs on the LAN side are not direcly accessible from outside your network, unless you open ports in the router to forward them to specific clients.
A Wireless router has both the functionalities of a router and an access point in a single unit.