In literature in general, are DFS and BFS considered to be special cases of best-first search?

Suppose the cost function is:

$f(n) = g(n) + h(n)$

Is it correct to reason that if and $g(n) = depth(n)$, then

If $\forall_n h(n) = 0$, we have a breadth-first search

If $h(n) = i$, where i is the number of nodes visited before visiting, we have depth-first search.

?

Are depth-first and breadth-first search usually considered special cases of best-first search?