Before revision:  While similar, these two concepts are equivalent only when the topology satisfies the following universal property: for each continuous mapping from preferences to outcomes there is a unique mapping from utilities to outcomes that is faithful to the preference map and is continuous.
After revision:  While similar, these two concepts are equivalent only when the topology satisfies the following universal property: for each continuous mapping from preferences to outcomes there is a unique mapping from utilities to model's outputs that is faithful to the preference map and is continuous.