Whether the wireless access point serves also as a router just depends on which type of WAP is used.
The type of wireless interface cards (b, g, or n) that these transmitters contain will determine how much and how far the wireless network extends or broadcasts.
The 802.11 standard designates the radio frequencies used and wireless access points (WAPs) serve as the connection point for both sending out and receiving wireless radio signals that then are physically joined to an organization's LAN. Wireless access points are in fact radio transmitters and represent a node, just like a computer, on a local area network (LAN). Chow, Timothy Bucknall, in Library Technology and User Services, 2012 Wireless access points and routers
