Bellman-ford we use data structure an array of size as no. of vertex and we update it looking at graph data structure in adj. matrix or adj. list. We run n times RELAX function for each edge. We never accept on each iteration the RELAXed value to be answer. We wait to run it n times. And we use the updated value of vertex weight in each iteration of data structure. i.e. This algorithm is completely rely on updating and using the stored value.
While Djkastra is based on finding best solution in each round. Which after n run combines to bring us the solution.