what kind of routing algorithms exists that are different to different to Dijkstra-concept?
Dijkstra (and A*,D*, bellman forge etc.) use this concept: Get the best Node from known Nodes, expand this and save the results to the known Nodes.
Are there any concepts that are fundamental different?
Bellman-Ford is fundamentally different. It uses dynamic programing instead of the Dijkstra greedy approach and works for graphs with negative weight edges.