I am working on a project that involves a deductive system $\vdash$, with two model-theoretic semantics $\models_A$ and $\models_B$, for which $\vdash$ is sound and complete. That is,
$\Gamma \vdash \phi$ iff $\Gamma \models_A \phi $ iff $\Gamma \models_B \phi$.
Here, $\Gamma\models_A \phi$ means the standard: for all $A$ models $*$, if for all $\gamma\in \Gamma$, $\gamma^*$ is true in the model $*$, then $\phi^*$ is true in the model $*$, and similarly for $B$.
Yet, $\models_A$ and $\models_B$ are not equivalent. For every $A$ model $*$ there exists a $B$ model $\circ$ that validates exactly the same formulas, but the reverse is not true. For example, either $*\models_A \phi$ or $*\models_A \neg \phi$, for any $A$ model $*$. But there are $B$ models $\circ$ such that $\circ\not\models_B \phi$ and $\circ\not\models_B \neg \phi$.
My question is, what is this phenomenon called?