  We characterize the graphs for which the independence number equals the
packing number. As a consequence we obtain simple structural descriptions of
the graphs for which (i) the distance-$k$-packing number equals the
distance-$2k$-packing number, and (ii) the distance-$k$-matching number equals
the distance-$2k$-matching number. This last result considerably simplifies and
extends previous results of Cameron and Walker (The graphs with maximum induced
matching and maximum matching the same size, Discrete Math. 299 (2005) 49-55).
For positive integers $k_1$ and $k_2$ with $k_1<k_2$ and
$\lceil(3k_2+1)/2\rceil\leq 2k_1+1$, we prove that it is NP-hard to determine
for a given graph whether its distance-$k_1$-packing number equals its
distance-$k_2$-packing number.
