# shortest distance vs shortest path

This question might be redundant but I want to verify my understanding further. Suppose I have this linear directed graph:

$$S \overset{2}{\to} A \overset{1}{\to} B \overset{3}{\to} E \overset{1}\to D.$$

Here, $S$ is the source, $D$ is the target, and numbers indicate to edge weight:

1. When taking about shortest path, do we only count the number of edges? So in this example, shortest paths from $S$ to $D$ is 4.
2. Thus, when taking about shortest distance, we find the sum of the edges weights. So in this example, shortest distance from $S$ to $D$ is 7.

The reason why I elaborate this question using example is that I've seen plently of answers when I google this question but it seems they treat the work path and distance in similar way which is counting the number of edges (hops).