ADSL modems are usually USB devices - the old Speedtouch 330 was a popular example. They have no inbuilt firewall, and usually inferior performance to ADSL routers. A very small number of ethernet-connected modems exist, but these are basically ADSL routers with the router function absent.
What we commonly refer to as routers in this context are modem routers, which have a modem facing the internet and a router between it and the computers. These have many performance and security advantages over simple modems.
There also exist plain routers which contain no modem. These are commonly used with cable systems, and can also be used in conjunction with an ethernet modem on ADSL systems, but for most ADSL users the combined modem/router is the easiest and best option.