The atom-bond sum-connectivity index $ABS$ is a recently introduced vertex-degree-based graph invariant, defined as the sum over all pairs of adjacent vertices $u,v$ of the term $\sqrt{(d_u+d_v-2)/(d_u+d_v)}$, where $d_u$ is the degree of the vertex $u$. A much older such invariant, the sum-connectivity index $SC$, is defined via $\sqrt{(1/(d_u+d_v)}$. We study the difference between $ABS$ and $SC$ and establish various bounds for it, in terms several vertex-degree-based graph invariants.