Dijkstra and A* Algorithms: Why is A* faster?
I absolutely don't understand the attached images and what you try to do on it. What I can say is that Dijkstra an A* algorithm are pathfinding methods:

Dijkstra algorithm is an exploration method that let you find the shortest path to any vertex of the graph. The idea is to always consider the vertices that you reach from the cheapest (closest) node of the queue.

You may run this algorithm to find the shortest path from a specific node $s$ to a specific node $t$. But you can also use it to determine global properties of the distances from $s$. Or for instance, build a tree that let you backtrack the path from $s$ to any vertex.

A* algorithm is basically a Dijkstra method that use an additional heuristic to sort the nodes of the queue. On distance problem, this heuristic is generally based on the euclidian distance from the node to the aim. It favorises the exploration of the nodes that are more likely to go in the good direction. So this specialization of Dijkstra algorithm is only used to go from a specific node $s$ to a specific node $t$. It is generally largely faster but does not guarantee to find the optimal path (in the ver).

I suggest you play with this  pathfinding simulation tool