Let $\kappa$ be a regular cardinal, and let $D$ be a small $\infty$-category which admits $\kappa$-small colimits. Then is the canonical map $D \to Ind_\kappa(D)$ an equivalence, and if not why not? I ask because Lurie's Higher Topos Theory Theorem 5.5.5.1 gives equivalent conditions to be a presentable $\infty$-category, and condition (4) seems to suggest to me that $D$ and $Ind_\kappa(D)$ are not equivalent (but Lurie does not say that). But I would have guessed they are equivalent since the $D$ has all $\kappa$-small colimits, and in particular it has all $\kappa$-filtered colimits, and so the identity map $D \to D$ factors as $D \to Ind(D) \to D$ by the universal property of inductive categories.
Also, I think my confusion has nothing to specific with $\infty$-categories; if you know the answer in the case of ordinary categories that is enough for me to believe.