Cable/DSL routers don't really have the full options for routing tables or configuration, and really don't have anywhere to "route" to, they only have one interface on each side. A real router is usually capable of at least two WAN interfaces, which can be of different types or the same, and often multiple LAN interface, and the router can be programmed with either static routes that define which interface gets used for which traffic, or can accept dynamic routing updates from another router based on which path is the best at any particular time (like if a remote network goes down). A real router can also simply do MORE of the things a cable/DSL router can do, like multiple NAT configurations and detailed filtering based on source, destination, et cetera.
There are of course different levels of "real" router. A Cisco 1601 is like a cable/DSL router, but for a T1 service (or two), connecting to a LAN. A Cisco 12000 series isn't often directly connected to a LAN, it is used as a routing point between multiple LANs and other routers. The difference is like coming to a fork in the road, you've only got two options, or coming to a city center with multiple roads in a spoke layout where you can go to several different places.