  We examine the relations between different capacities in the setting of a
metric measure space. First, we prove a comparability result for the Riesz
$(\beta,p)$-capacity and the relative Hajlasz $(\beta,p)$-capacity, for
$1<p<\infty$ and $0<\beta \le 1$, under a suitable kernel estimate related to
the Riesz potential. Then we show that in geodesic spaces the corresponding
capacity density conditions are equivalent even without assuming the kernel
estimate. In the last part of the paper, we compare the relative Hajlasz
$(1,p)$-capacity to the relative variational $p$-capacity.
