In your examples the active and passive sentences do not have exactly the same meaning.
If she is training to do something, them she is indeed being trained, but we are looking at the situation in a different way. Very crudely, in the active sentence, she is doing the work; in the passive sentence, somebody else is.
Some other verbs do have an active sense when used transitively, and a ’passive’ sense when used intransitively:
I am boiling the water.
The water is boiling.
Even here, the intransitive use of the verb does not convey the same sense as the passive (The water is being boiled) With the passive, we are aware of an agent, even if that agent is not particularly important. With the intransitive verb, the agent is irrelevant.