To me there is no difference between the two terms as they concludes one and the same thing. Auditing Standards use both terms to mean one and the same thing. But it has been observed that the term Unmodified opinion is used more often in standards instead of Unqualified opinion.
Some authors try to differentiate between these two terms as follows:
Unmodified opinion is the opinion where auditor expresses an opinion that financial statements are presented, in all material respects, in accordance with applicable financial reporting framework.
Unqualified opinion is the opinion where auditor expresses an unmodified opinion (as above) AND attaches an Emphasis of Matter Paragraph.
Simply, unmodified opinion is a clean opinion where as unqualified opinion is a “modified” clean opinion with emphasis of matter paragraph.
But to my mind we should not try to differentiate the terms in such way. The reason is that if we refer to Para 7(d) of ISA – 706 it is clearly stated that if auditor has included an Emphasis of Matter paragraph in the audit report than he must also indicate that opinion has not been modified in respect of the matter emphasized. So, this alone is enough to clear at any confusion regarding unqualified opinion and unmodified opinion. Therefore, both terms mean one and the same thing.