Wireless Routers

I'm not sure what the difference between WIFI and Wireless is.. in my mind, they are the same... unless you mean Cellular wireless... then it's different.  One uses the cell phone company to connect, one uses an 802.11x protocal to connect through a wired network.

As for keeping security with Access points, all access points have the ability to enable encryption at varying levels, and it is highly recommended that you do so.

WIFI doesn't mean anything its short for wireless.  What recommendations for business,  just make sure you have a router that does WPA encription.  WEP encription is easily cracked and should not be used.  WPA is the new standard and is secure.  An access point is the wireless router,  the name means what it means, access point for people to connect with a wirless network card.  802.11g is the newest standard and not expensive at all...it offers 54mbps and is WPA capable.  A linksys wireless router is fine for a office.

A wireless router and wireless access point are NOT the same thing.  A wireless access point is a device that you can plug anywhere into your network, and wireless clients can gain access.  A wireless ROUTER requires router settings to be configured to route properly, and would generally only be used at the outside edge, or, between segments of your network.

So would an access point increase the range of the wireless router? If so, then would the access point be managed by the wireless router?

As cbromley stated, a router would generally be used at the edge, or between segments.  Say you have a basic network, and have a wireless router as the gateway.  Yes, you could add additional access points to increase the range.  An access point can be plugged into another data jack, or if it's close enough to the router, it can be "bridged" to extend the wireless access without having to plug into a data jack.  The access point would not be "managed" by the router.  Each device will have its own configuration.