In my country, the state provides a cert to the applicant stating that his background is sufficiently clean. No more details. You can't tell if I am spotless or have done jail time but it was long enough ago not to matter anymore.

It does containg language like ... has no criminal record, except for child molestation etc... Which doesnt mean we're a country full of perverts, only that it can't be trusted for jobs working with children, another cert is used for that.

They can be explicitly requested by the employer or required by the law.

I had to provide the criminal background and prove my studies to my current employer.

I also had to pass a medical examination to obtain a certificate of eligibility to work.

They are provided by the applicant anyway, you don't do secret background checks, at least you shouldn't.

Indeed in my nation you can't. You can ask the candidate to give you some self-certification of it which would put him under criminal trial if he lied, but you cannot contact any third party and ask for direct information (nor get an authorization to ask for direct information) about another person

Most developed countries don't do BG check's for tuppenny ha'penny (trivial jobs) jobs in the same way the USA does.

In the UK its only for working with kids and jobs requiring a proper security clearance.