MI5 and MI6 are two British security agencies. As you would expect, one of the major differences between most security agencies is that they are not always the same in terms of operations and services being rendered. One of the major objectives behind the creation of MI5 is for the protection of the parliamentary democracy of Britain and its economic interest.
Also, MI5 was created to protect British citizens from terrorism and to run a very vibrant counterintelligence unit in its operations and for other sister agencies. In other words, MI5 was created to manage the internal or domestic security issues within Britain. On the other hand, MI6 was created to protect the country from external or foreign threats.
The agency acts mostly by providing foreign intelligence that will be useful in protecting the country from any external attack. Another name for MI6 is Secret Intelligence Service. At times, MI6 can wade in to gather intelligence about certain political issues in the country.