
A professor of mine once said "The difference between a Computer Engineer and
a Computer Scientist is about $5000" meaning the Engineer makes $5000 more than
the CS.
Seriously though the main difference is that most CS people write programs that
people will use, i.e. database, graphics, word processors, etc., while an
engineer writes for machines or control systems, i.e. the "computer" in your
car, a flight control system, computer controled devices, etc. In other words
CS writes SOFTWARE while CSE writes FIRMWARE. 
These are generalizations but for the most part that is what the difference is.