What is the difference between a career in pure chemistry and chemical engineering?

Ok, I don't know why the other answerer is talking about analytical chemistry....  To answer YOUR question:

HISTORICALLY, the difference was that chemical engineers built chemical plants, and chemists did the "science."  A lot of things that the chemical engineers did, like most engineers, were very analytical.  Complicated equations for liquid flow around pipes, predict pressures a plant would survive without exploding, build scale models, etc.  The chemists did a lot of fundamental science.

TODAY, the differences have changed.  Although there are still many chemical engineers building chemical plants, a lot of them said "hey, liquid flowing in a pipe...  did someone say 'blood'?"  At which point biomedical engineering was born.  Biomedical engineering is chemical engineering applied to biological and medical problems.  This includes designing artificial limbs, blood vessels, small diagnostic devices, drug delivery systems, etc.  Much of this type of work inherently requires fundamental science.  Chemists, on the other hand, have also been branching out into biology, materials science, etc.  And some of them have very promising basic science, so they start pursuing applications for them, sometimes in collaboration with chemical/biomedical engineers.

I for example, started my PhD in the Chemistry department of a university.  The university has a close relationship with a major national laboratory, and so my advisor is officially in a building belonging to the Physical Biosciences division of that laboratory.  I am about to graduate with a PhD, and do post-doctoral work for a woman who is moving from the Chemical Engineering department in one university to the Biomedical Engineering department in another university.

The traditional disciplines are really blending pretty quickly.  You will often find that what is "chemical engineering" in one university is "bioengineering" in another university, "materials science" in another university, etc.  If you want to gain a better idea look at various departments at schools across the country, and get a feel for the range of things that people do.

Good luck.

Pure Chemistry deals with Research and Development mainly while Chemical Engineering deals with chemistry applied to manufacturing process.

chemists work in a laboratory, chemical engineers build chemical manufacturing plants.