Negative weight cycle means that whenever we go through the edges of the cycle, i.e., take one cycle or more, the distance/weight to reach such vertices will reduce from earlier. Thus, for every round of the cycle the path cost is reduced, which is not true in real scenarios. This happens because a cycle allows us to go via same edges more than once.
Negative weight edges means they are not forming a cycle. Thus, we won't go through a negative edge more than once. This won't be a problem.
Djikstra algo fails with negative weight cycles but not with negative weight edges, it is because Djikstra algo can't determine if negative weight cycles are present in the graph or not. Bellman-Ford can be used in such cases.
