Why BFS is source vertex specific? Take a graph $G=(V,E)$ .

As we know both DFS and BFS are graph search algorithms . 

But why the algorithm for BFS is designed in such a way that it does not cares about the vertices that are not connected to the source vertex  $s$  but DFS takes care about all vertices in $V$.

I mean if $G$ has $l$ connected components and a vertex $s$ is in one of the connected component among $l$ , then if $s$ is the source vertex for BFS , then BFS performs only traversal on the only one connected component (which contains $s$).

If $G$ is input for BFS , it constructs one BFS tree (for component which contains $s$).

But in case of DFS , it constructs a DFS forest with $l$   DFS trees.

Why no BFS forest and it is restricted to a specifc component (containing $s$)?  Any reason involved ?

For Bfs algorithm page # 595 and for Dfs algorithm page # 604 from here
Both BFS and DFS are algorithms for exploring a single connected component, and there are also several others. All such algorithms can be extended to explore all connected components in a graph.