Let $X$ be an algebraic stack. In Perfect complexes on algebraic stacks (4.1) a *perfect complex* $P \in \mathsf{D}_{\mathrm qc}(X)$ is defined to be a complex such that, for any smooth morphism $\operatorname{Spec}(A) \to X$ (where $A$ is a commutative ring), the complex $\mathbf{R}\Gamma(X,P_{|\operatorname{Spec}(A)})$ is a perfect complex of $A$-modules.

On the other hand, if $X$ is just a scheme, then a complex $P \in \mathsf{D}_{\mathrm qc}(X)$ is called perfect if it is quasi-isomorphic to a bounded complex of locally free sheaves of finite rank.

Question: if $X$ is a scheme, how can I prove that the two definitions agree? Is there a reference with a proof of this fact?