Generally, it depends on the level of clearance you are applying for.
Also, how serious your offense was, and how long ago this was, will determine how “un-recorded” even a conviction, that has been recorded as “not recorded”, actually is.
Ultimately, everything is recorded (eg for TS/S-NV1/2-PV1).
However, even a recorded conviction is not the end of the road.
If it has been greater than 10yrs without re-offending (5 for juvenile offenses), and there was less than ~3 years imprisonment (*of any “kind”); sometimes you will not have to mention a conviction. This is called the conviction “spent” time.
The Federal Police (AFP) can provide further information on if your convictions are covered under the spent conviction scheme.
Sometimes the question will be vague – in which case there is some situational discretion. In most cases, questions will be specific enough that this is not confusing.
However, an employer does not necessarily have the right to “ask”, if it is not germane to the duties you will be employed to discharge. (*though this is not the same as an employer being unable to find out).
You may apply for your own National Police Certification if you are uncertain of your status.
For further information on criminal records, there is a legal aid entry.
All clearances in Au are otherwise handled by the AGV, regardless of department.