An Apostille is a certification of a document (authentication) that is done through the state, please call the US Dept of State at 202-485-8000 or visit www.travel.state.gov for more information.

A certificate of good conduct is a document that shows an individual has no criminal record. It can be used for many reasons, including adoption, school, and work abroad.  More information can be found on the Dept of State website https://travel.state.gov/content/travel/en/international-travel/while-abroad/criminal-record-checks.html