Distance = How far
Vector = Direction
The distance is typically measured using hop count. The best known Distance Vector protocol is RIP, this measures distance with hop count (how many intermediate routers there are to the destination network). They only learn the network from their directly attached neighbors which gives rise to the description of routing-by-rumour as RIP does not create a complete map of what is going on in the network.
The most famous and possibility ubiquitous DV (Distance Vector) protocol is EIGRP (Enhanced Interior Gateway Routing Protocol) which is an Advanced DV protocol. It however doesn't use Hop Count as a metric; it uses bandwidth and delay.
RIP is extremely easy to set up and is best suited to very small networks where the will be very - if any - changes to the topology.
EIGRP is an extremely powerful and functional routing protocol.
Link State protocols differ from DV protocols because they create a map of the entire network topology. Due to the fact that every router has a full topology the memory and processor resources need to be greater. The most commonly used Link State protocol is OSPF (Open Shortest Path First) which is also the most commonly used IGP in networking today
Link State protocols take into account the entire route/path to the destination network and use that information to decide the best route to take. The slowest link on the path will be used to calculate the metric for the route.
Designed to route the internet. A massive network that connects millions of routers together. The Path Vector protocol is called BGP (Border Gateway Protocol). It is routed along a path of ASs (Autonomous Systems) each AS will be a group of networks. Loop prevention is simple in BGP, if an AS appears more than once and the repetition is non-consecutive then there is a loop. A path can contain the same AS number more than once consecutively and not be considered a loop as this is generally done on purpose to manipulate routing by increasing the length of the path.