This has absolutely nothing to do with verb tenses or active or passive voice.
The usual, normal, interpretation of those sentences is:
The dog chased the cat. dog = subject, cat = object
The cat chased the dog. cat = subject, dog = object
Only by unnaturally stressing the first part of the sentence, and providing a whole lot of context, it would be possible to interpret the sentences as having the object coming first.
In English, the position of the subject and object relative to the verb is immensely important. In other (usually inflected) languages, it would not be very difficult to switch the place of object and subject without changing the meaning of the sentence, but in English, that is a very tough, if not impossible, feat.
As for the passive voice, that is a whole different matter. Your sentences would be transformed like this:
The dog chased the cat. => The cat was chased by the dog.
The cat chased the dog. => The dog was chased by the cat.
You are correct in noticing that in the passive versions of the sentences, subject and object are inverted, but just inverting them does not make the sentence passive! You need to change the verb as well!