There are two completely different (but related) things…
An access point (AP) is a device that allows you to “connect” one medium to another, for example, you have a wired network and you connect an AP to it to allow for wireless “clients” to connect to the wired net. The concept works the same for WiFi, Bluetooth or any other technology.
A router is a device that allows for “packet distribution or traffic control” on a network, for example when you have a local net with a gateway to an external net, the router would be in charge of “routing” the packets to the proper interfaces depending on the destination.
What is usually called “a wireless router” is in fact a combination of devices, like a NAT, a wireless access point, a DHCP server, a switch, etc, all into the same box.
So….. Bottom line, if you want to share a single internet connection with several machines, including one or more wireless machines, then use a “wireless router”. If you already have a physical network running, with perhaps the internet connection shared by another device, use an AP.
Regards,
Marcelo