Almost all "interpretations" (using the word as used in the literature) of quantum mechanics use different axioms, and its a mathematical question as to whether or not the theories make the same predictions. Many stochastic "interpretations" modify the Schroedinger equation, for instance. Even many-worlds can't be proven as an interpretation using your definition (no one has shown it actually leads to the same predictions as Copenhagen).

Its an unfortunate artifact of the literature on various approaches quantum mechanics that the words interpretation and theory often over-load each other, but its the reality we live in.

If that's your definition, then it's an empirical question whether a given model is an interpretation, because it's often contingent and difficult-to-demonstrate that a given ontology is necessarily 'invisible', as opposed to 'potentially-testable-but-as-yet-untested'. Impossibility proofs about future scientific experiments are no easy task. So we can only speculate about whether Many Worlds, Bohmian Mechanics, Collapse theories, etc. are 'interpretations' in your sense.

(And by 'invisible' I gather you mean 'empirically equivalent to a certain set of rivals' -- so whether something's an interpretation is always relative to other models, the real predicate is interpretation-compared-to-x.)