Modem- give you internet on lan/wifi/usb as o/p from telephone adsl line input.
Router-Splits the input across output.For eg the output of modem can
be given to router.The router can now share that as output on multiple lan
ports and wifi.
*www.microsoft.com/library/media/1033/windowsxp/images/using/networking/setup/68573-router-diagram.gif