Software quality and security assurance both concern risk to the organization, but they do so for different reasons. Risk might be mission critical such as software on a scientific robot crawling another planet. Or risk might be associated with sensitive financial information. In the first example the integrity of the software is paramount; it is hard to fix something on another planet. In the latter example both quality and security are important, with security perhaps paramount.
There’s also a fundamental difference in how quality and security are each regarded. A quality assurance test at the end of a production cycle will tell you whether a software product is stable enough for release – a simple “Yes” or “No.” Whereas a security test will be more vague – “It depends” – and in the race to market, that result may be overridden by management. Quality code may not always be secure, but secure code must always be quality code.