A routing Table is a table which contains the best paths, that a router uses to forward packets. You can also say it’s a decision making table, what ever the routing protocol or mechanism is being used by the routers they decide where to forward the packet on the basis of routing table.
Some times it’s also called a forwarding table.
While topology table is a table that can be defined as a road map of any network topology, which contains all the possible routing information and all the paths, good or bad but all the paths(routes/networks). But Topology table is not used by some protocols. In the case of EIGRP and OSPF ,yes!! They both use it!! Topology Table is used to find the best paths,and every protocol run their algorithms, on the Topolgy table, but the topology table is never used for the final decision it’s just used to build the best paths and routes according to specific protocols, which ever the algorithm the y use!!!!
In Eigrp Topology Table is called Topology Table, and it contains all the possible information about all the networks/paths/routes, that a router has learned from it’s neighbors., gus or ba , but all paths. EIGRP Topology Table contains back up paths also called Feasible Successors(Remain in Topology Table, Making EiGRP Fastest!!) and Successors ( best paths, copy of it is included inside Routing Table).
In ospf Topology table is also named as LSDB, or Link state Database. It has the same function, keeps all the information of all the possible routes inside an OSPF Area. in eigrp there is no area concept, but OSPF uses Areas concept. And an Area is a group of routers having same LSDB!!
In OSPF there is no back up path concept, so OSFP LSDB doesnt contain any backup paths. That’s why ospf convergence time is slower than EIGRP!!