Two recurrences for the change-making problem with repetition
First, the number of subproblems and dependencies among these subproblems for the first recurrence are $v$ and $nv$ respectively, while they are $nv$ and $2nv$ respectively for the second one. 

Pictorially, the subproblem-dependency graph of the first recurrence is a 1D array and that of the second one is a 2D table.

Informally, the subproblem-dependency graph of the second recurrence can be regarded as a "compacted" version of that of the first one in the sense that the 2D table is compressed into a 1D array through the clause $\lor C[i−1,w]$ in the second recurrence.

Formally, inspired by the comment made by @Raphael, if we expand $C[i−1,w]$ recursively in the second recurrence, we get (ignoring the $w \ge x_i$ details)

$$
\begin{align*}
  C[i,w] &amp;= C[i, w-x_i] \lor C[i-1, w] \\ 
         &amp;= C[i, w-x_i] \lor (C[i-1, w-x_{i-1}] \lor C[i-2, w]) \\
         &amp;= C[i, w-x_i] \lor C[i-1, w-x_{i-1}] \lor C[i-2, w-x_{i-2}] \lor C[i-3, w] \\
         &amp;= \cdots  \\
         &amp;= \bigvee_{j \leq i: x_j \le w} C[j, w-x_j]
\end{align*}
$$

Therefore, we can conclude that $C[n,w] = C[w]$.