More accurately, the routers that are on offer generally include the modem portion (i.e. have an ADSL port). You can also get so-called WAN routers which have an Ethernet port instead of the ADSL port.
In the past, it was possible to get e.g. USB-ADSL modems, but these are few and far between nowadays. Most people, when referring to ADSL modems, are talking about an ADSL-Ethernet device, with just a single Ethernet port. These are actually also ADSL routers, because they allocate a private IP address to the host(s) connected to the ethernet port, and "route" that IP address out over the ADSL interface.
The major difference, then, between a single port ADSL-Ethernet router, and the more featureful ADSL routers with 4 ports and WiFi, is exactly that. The bigger devices allow wifi clients to connect to them, and support more than one ethernet client connected directly to the router. If you want to be able to do this with a single port ADSL-Ethernet router, you would need to provide your own ethernet switch, and your own wifi access point.
More sophisticated users may prefer to get an ADSL-Ethernet router, and provide the rest of the portions themselves, as this allows them to choose precisely the features that they want, which may not be available in the mass-market combination devices. For instance, they may want more than 4 gigabit ethernet ports, and not care about wifi. So, buying a cheap 8-port gigabit switch, and a single-port ADSL-Ethernet router would suit their purposes better than a combined device.
In your case, I'd suggest getting a simple ADSL router, including Wifi, because at some point in the future, you are likely to want to let your phone connect to ADSL rather than using 3G all the time. These are available quite inexpensively, around R300-R400, which is not much more expensive than the cheapest single-port ADSL-Ethernet routers.
