In areas of quantum mechanics related to information theory, open quantum systems, and foundations, I've seen the formalism of density matrices employed to model two distinct physical scenarios
Scenario 1: I have a quantum system in some pure state $|\psi\rangle\in\mathcal{H}_\text{system}$, corresponding to a density matrix $|\psi\rangle\langle\psi|$. This state can undergo decoherence by coupling with an environment, corresponding to a Hilbert space $\mathcal{H}_\text{env}$. Decoherence results in information loss, transforming the pure state into a mixed state $\rho$ by some CPTP map $\mathcal{E}$ that describes the decoherence $$ |\psi\rangle\langle\psi| \mapsto \rho := \mathcal{E}(|\psi\rangle\langle\psi|). $$ Here, a fundamental result is the dilation theorem, which implies the existence of a unitary $U$ acting on $\mathcal{H}_\text{system} \otimes \mathcal{H}_\text{env}$ whose restriction to $\mathcal{H}_\text{system}$ is the CPTP map $\mathcal{E}$.
Scenario 2: I have a quantum system in a state $|\psi\rangle \in \mathcal{H}$, and I apply a unitary $U$ from some set of unitaries $\{U_i\}_{i\in\mathcal{I}}$ (we'll assume $\mathcal{I}$ is a finite set for simplicity). However, for whatever reason, I don't know which unitary I applied, because maybe the unitary was chosen randomly or I simply forgot. Thus, the resulting state is now a mixed state $\rho$, which can be written as $$ \rho = \sum_{i\in\mathcal{I}}Pr(i) U_i |\psi\rangle\langle\psi|U_i^\dagger,$$ where $Pr(i)$ is the probability that $U_i$ was applied.
In other words, density matrices are used to model decoherence due to coupling with an environment, and simple epistemic certainty in an experiment.
My primary question is: is there any meaningful distinction in the application of the density matrix formalism to these two scenarios, either mathematically, physically, or otherwise? One of the reasons I am curious about this is, we can in principle apply the dilation theorem in scenario 2 to give us a unitary $U$ on some larger Hilbert space $\mathcal{H}\otimes\mathcal{H}_0$ whose restriction to $\mathcal{H}$ is the CPTP map that describes the application of a random unitary from $\{U_i\}_{i\in\mathcal{I}}$ to $|\psi\rangle$. This would seem to imply that both scenarios are physically the same, as the ''epistemic uncertainty'' map described in scenario 2 can be modelled as a decoherence process as described in scenario 1.