A Compliance audit is typically an audit which compares a company s defined systems against those required by the standard being audited against.
May be extensive such as with a QS-9000 (now IATF 16949) audit, or may be a customer audit which is very limited in scope.
Typically you look at the requirements of the standard or requirement and contrast them against the company s systems.
Typically a Compliance (Conformance) Audit is done as a Desk audit. This is verification of compliance.
When a registrar does a Quality Manual Review prior to the pre-assessment audit (usually at US$750 to US$1500), for all intents and purposes they are doing a Compliance Audit (does the manual address every line item of the standard being audited against).
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There is an interesting thread in which these issues are addressed:
ISO 19011 - Quality and Environmental Management Systems Auditing Forum Discussions