Modem - Brings internet from your ISP (Globe, Smart or PLDT) to your house.
Router - Uses the internet provided by your ISP (Globe, Smart or PLDT) and splits it or "routes" it to 2 or more devices.
Most modems given ng mga isp ngayon is a 3in1 combo. For example yung globe at home prepaid wifi has a modem, router, access point and a switch. In one device. Though normally these devices suck in delivering great speeds, literally, pero may makikita ka rin naman nang magandang device na 3in1 combo.