Distance Vector Protocols operate on the principle of "routing by rumor." Each router shares its entire routing table with its directly connected neighbors at regular intervals. When a router receives a routing table from a neighbor, it updates its own table with any new or better routes. The "distance" is typically measured by a metric like hop count. Simple but can be slow to converge and is susceptible to routing loops (RIP).
Link State Protocols provide each router with a complete map of the network topology. Instead of sharing their entire routing table, routers send out information about the state of their own links (e.g., connected neighbors and the cost of the connection) to all other routers on the network. Using this information, every router can independently build an identical map of the network and calculate the best path to every destination. This approach leads to faster network convergence and is more scalable than distance vector protocols (OSPF).