I am not sure about medium-risk public trust positions, but for high-risk public trust positions (think access to PII, social security # type stuff) they require an in depth personal history, including a meet and greet with an investigator (usually ex-law enforcement, so I was told).

Protip: Contractor or FTE, make sure you specifically ask HR whether or not there will be an additional screening, and whether or not it is a 'public-trust' position and what level that would be following your hiring.

I was pretty miffed when 'they' told me after the fact that my position required an additional background check and that my continued employment would be predicated on the outcome.