The Financial Services Agency's October 2018 paper gives three examples of cases where conduct risk arises: adverse effects on user protection, adverse effects on market fairness and transparency, and adverse effects on the institution's own reputation. A common understanding of conduct risk has not necessarily formed, and the FSA does not require institutions to use the concept.
The Financial Stability Board (FSB) says that misconduct can be generally understood as conduct that falls short of expected standards, including legal, professional, internal conduct and ethical standards. This site writes "misconduct" for the conduct itself and "conduct risk" for the risk that it occurs. In a 2018 report, the FSB gives retail mis-selling and collusion in the manipulation of wholesale markets as recent examples of misconduct.
The regulatory definition of operational risk excludes reputational risk, so conduct risk partly overlaps with it and partly does not.