No trace means you were never convicted of any recordable offense in the UK. It will not show if you were ever arrested or charged for an offense that you were eventually acquitted from, but you are still required to disclose such events in your applications if that has happened to you.
What your advisor has told you isn't necessarily wrong but it isn't accurate either. It doesn't matter what 'type' of conviction you get abroad whether felony, misdemeanor, summary, traffic offense, civil ticket or even if you were convicted as long it can be shown that there is a reasonable ground to believe you committed the offense. However if the offense has no direct equivalent under Canadian penal code then it will be treated as if it doesn't exist and will not affect your application, only the offenses which have an equivalent counterpart count.