Modems and routers are both involved in connecting your home PCs to the Internet. The modem encodes and decodes data so that it can pass between your home network and your Internet Service Provider (ISP). The router, on the other hand, directs the information collected by the modem to devices within that network. The modem brings the information in, and the router distributes (or “routes”) it to different devices like computers and phones.
A router allows computers to connect to the modem and to each other in a network. It selectively delivers packets of information to multiple destinations, and allows multiple devices to connect to the Internet via the modem.
A modem can only connect to one device: either a home PC or a router.
A modem does not screen the data it encodes or decodes, and so it passes on any potential threat to connected computers.
Routers examine data packets to determine their destination, and so can contain firewalls to screen out attacks on the network.
Depending on the style, features, functionality and the brand, the price of a Router can range anywhere from $10-$74,000+. Prices for Modem range from $5-$23,000+.
You can find current prices on Amazon:
edit Video explaining the differences