There is potential for confusion here.
A few years ago, an "ADSL modem" would be just that: a modem which connects to the ADSL line at one end (basically, plugs into the BT master socket) and would provide an ethernet (RJ45) connector at the other. One popular example is the D-Link 300G+ and I have two of those right here (they work well).
But: while such a modem would be all that's needed to give your PC internet connectivity, it left it wide open to the internet. The average time to getting infected, via such a connection, would be measured in minutes. (About the same as if accessing the internet via a plain 56k modem, actually...)
Then "modems" started to get more clever. D-Link brought out an "identical" box called the 300T which was a modem but also did NAT (network address translation) plus had a DHCP server. It was actually an 80x86 PC chipset inside, running the usual ripoff Linux code which most today's consumer IT gear is based on. Such a modem - effectively a full NAT router but with only one ethernet port; most consumer routers have four ethernet ports - protected the PC pretty well.
A lot of people bought the 300T and tore their hair out trying to make it work, not realising that its extra functionality needs configuring correctly.
Today, few normal people deliberately use separate ADSL modems, but the animal survives in the form of a cheap and dirty USB-attached modem which is bundled with the very cheap broadband packages. It uses USB rather than ethernet to make the config more trivial.
Most smart consumers today buy an ADSL router which normally incorporates the ADSL modem internally, and gives you four ethernet ports, plus usually a wifi access point too. These boxes are about £50 and everybody and their dog makes them.
The only time one would use a standalone ADSL modem, like the old 300G+, would be if using a more high-end router or firewall or a VPN box or whatever and these don't normally have built-in ADSL modems.