What is the difference between a systems engineer and a systems administrator?

The two titles are used so interchangeably they've lost all meaning.

Some people will argue a systems engineer outranks a system administrator, and that may be the case in some workplaces, but you can't definitively go by that.

For instance, my current, fairly large workplace assigns the same salary grade to systems engineer, systems administrator and systems analyst. HR originally had specific job duties for each of these, but it is relatively random. We also have the same salary grade for a senior systems engineer/admin/analyst.
Read more: Salary and Compensation of IT Administrators

At my company, a systems engineer is supposed to be developing systems from the ground up, like some of our HPC work, sysadmins tend to be closer to hardware (linux OS or VMware for instance), and systems analysts tend to deal with applications (Exchange, Sun LDAP, CRM). But you'll find people with the "wrong" title on project teams. They're all the same salary grade so in the end it isn't a crisis.

Anyone who can tell you specifically what these titles mean is full of it, since it's going to be different at every company.