For FIVB-conformant matches:
The team has to specify the error to verify. If the error is has not occured the team loses the challenge. This is also the case if another arbitrary error occurs. Only the error specified by the team is checked.
This has already lead to such funny situations as you described.
There is a list of verifiable errors here, along with a more detailed description of the video challenge rules.
Unfortunately, it lacks information answering your actual question.
I'll look for a specific quote to second that.
I am sure because I've eye-witnessed that all (including the "funny" situation) while watching a FIVB match, that is, on international level.