To cut long story short, a security analyst is more concerned with breaking the system whereas a security engineer is concerned more with fixing these systems. To elaborate more on this point, you will find a security engineer attempting to deploy security solution to the system as an attempt to make it secured as much as possible. This involves deploying some tools like firewalls, IDS, etc into the organization’s system. On the other hand, a security analyst will not be excited about something more than his excitement about finding the weaknesses and vulnerabilities within the system through performing tasks like pen-testing, auditing, etc.
It is also worth noting before we move on, that employers always do not make that much of a difference when they post their job and they just mention their need for a “Security Analyst/Engineer”.