The all-pairs shortest path problem asks: what is the shortest distance between every pair of vertices in the graph?
If you have vertices, you need to compute distances. One approach is to run Dijkstra from each vertex, giving time. Floyd-Warshall solves this in time with simpler code and handles negative edges (as long as no negative cycles exist). For dense graphs or when you need all distances, Floyd-Warshall is the standard choice.
Space complexity is for the data structures used.