The logical next step from static routing is dynamic routing. When we talk about dynamic routing, we classify the routing protocols into two main groups.
The distance vector protocols are said to advertise ‘vectors’ of information. That is, a distance and direction. In IP terms, that would be a metric and an interface. The distance vector protocols (relevant for the CCIE) include RIP and EIGRP. Distance vector protocols are often considered to be ‘routing by rumor’. A neighboring router sends a router some information and says “You can get here by coming to me and it’s this far away”.
Link state protocols are a little bit different than distance vector. Link state protocols hear updates for all router’s participating in the same routing protocol instance. That is, each router generates it’s updates as well as forwards updates that it hears from other routers. In this manner, each router knows about the entire routing topology rather than only what it hears from it’s directly connected neighbors. Routers running a link state protocol are able to map the entire network, then run their own calculations to determine the best path to each network. Examples of link state protocols include OSPF and IS-IS.
There are more nuances to each type of routing protocol but I think it’s best to flush those out as we examine each. The major differences between distance vector protocols and link state protocol are important to remember.