I've read in Introduction to algorithms(CLRS) that Dijkstra's algorithm uses ideas similar to those of BFS? I think it really makes sense with respect to Dijkstra's algorithm with relationship to BFS when there are multiple short paths. Consider the following problem for conclusion if you can see.
Yes the shortest path trees produced by djikstra's and BFS are identical in the case where the graph edge weights are represented by hop counts or in other words all the edge weights are 1 . Multiple Short Paths don't actually signify any relation with BFS . For finding the shortest Paths with BFS in a weighted graph we have modified versions of the algorithm.