modified report and modified opinion

The auditors opinion is contained within the audit report. An audit report consists of four basic parts
1. Statement that auditor audited financial statements for the period.
2. Management’s responsibility
3. Auditor’s responsibility
4. Opinion

Where an opinion rather than an unqualified opinion is given, then the report is modified.
1. A qualified opinion (material but not pervasive): Basis for qualification is given. Opinion states that except for the basis for qualification the financial statement gives a true and fair view
2. A disclaimer opinion (limitation of scope or uncertainties): Basis for disclaimer given. Opinion states that “we do not express and opinion on these financial statements”
3. An adverse opinion (material and pervasive): Basis for adverse opinion given. Opinion states that because of the adverse information, the financial statements do not give a true and fair view.

So to answer your questions in a nutshell
1. modified opinion = modified report
2. modification in audit opinion = modification of audit report
3. unqualified audit opinion = unmodified audit report.

Alkemist is not quite right,

If an opinion is modified (except..for, disclaimer, adverse) then the audit report has been modified.

However, a report can be modified without the opinion being affected. For example, an emphasis of matter paragraph can be added to the report, but this does not modify the opinion. It simply is there to draw attention to something properly disclosed in the notes.