  In recent years, the existence of a hadronically stable $\bar{b} \bar{b} u d$
tetraquark with quantum numbers $I(J^P) = 0(1^+)$ was confirmed by first
principles lattice QCD computations. In this work we use lattice QCD to compare
two frequently discussed competing structures for this tetraquark by
considering meson-meson as well as diquark-antidiquark creation operators. We
use the static-light approximation, where the two $\bar{b}$ quarks are assumed
to be infinitely heavy with frozen positions, while the light $u$ and $d$
quarks are fully relativistic. By minimizing effective energies and by solving
generalized eigenvalue problems we determine the importance of the meson-meson
and the diquark-antidiquark creation operators with respect to the ground
state. It turns out, that the diquark-antidiquark structure dominates for
$\bar{b} \bar{b}$ separations $r < 0.25 \, \text{fm}$, whereas it becomes
increasingly more irrelevant for larger separations, where the $I(J^P) =
0(1^+)$ tetraquark is mostly a meson-meson state. We also estimate the
meson-meson to diquark-antidiquark ratio of this tetraquark and find around
$60\% / 40\%$.
