The 3G modem is a device that allows users to connect to the internet via the 3G mobile network that is used for mobile phones. There are currently three types of 3G modem available and these are the data card, the USB modem stick, and the 3G USB dongle. The 3G modem connects to the mobile network through a range of mobile broadband service providers like Vodafone, Orange, O2, and other similar companies.
A router(to differentiate it from the tool used to rout wood), is a purposely customized computer used to forward data among computer networks beyond directly connected devices. (The directly connected devices are said to be in a LAN, where data are forwarded using Network switches.),Refer: Wiki site