Word ladder problem for words with different length
Your algorithm that runs breadth-first search (BFS) on the graph built with words as nodes and pairs of words that differ by one letter as edges is the natural algorithm to solve the problem, whether the words are different lengths or not. 

I would just call call your algorithm as a BFS algorithm. It is classic application of BFS to search for the shortest paths between two nodes of a graph where the length of a path is simply the number of its edges. 

If we let the BFS algorithm run until all nodes has been visited, then it will be able to find all shortest paths between a source node and all other nodes.

You can find some detailed comparison between BFS and Dijkstra algorithm for shortest path in a graph here.