We compare two frequently discussed competing structures for a stable $bar b bar b u d$ tetraquark with quantum numbers $I(J^P) = 0(1^+)$ by considering a meson-meson as well as a diquark-antidiquark creation operator. We treat the heavy antiquarks as static with fixed positions and find diquark-antidiquark dominance for $bar b bar b$ separations $r < 0.2 , text{fm}$, while for $r > 0.5 , text{fm}$ the system essentially corresponds to a pair of $B$ mesons. For the meson-meson to diquark-antidiquark ratio of the tetraquark we obtain around $58%/42%$.