PSU entity can be in the form of company , corporation or government department 
if its company its same as regular company
if its corporation is depends on law applicable 
if its government department — CAG does it and CAG is focused on appropriateness of decisions and transactions apart from appropriateness of books & financial statements 
in regular audit auditor is generally not concerned with appropriateness of business decisions and transactions 

compliance audit — whether government decisions and transactions are appropriate as per constitution , rules framed there under for cabinet and parliament , whether they contradict any law etc it also involves evaluating law also
propriety audit — going beyond rules and regulation and check whether expenditure is giving real benefit to public at large.
Eg School constructed with all approvals but there is no road to access it is waste of money and not a proper
Performance audit focus on economy, efficiency , effectiveness of government scheme or any government entity , generally 3-5 years of performance audit is done at a time