I see people use both in their job titles. Which one is correct?
Both. Nobody cares.
So long as you're not massively misrepresenting what you did, the only point at which anyone is ever going to care about exactly what your job title was is if they are attempting to verify your work history, and even then they're not going to care about "engineer" vs "engineering". If you're still worrying about this, use whatever is listed on your contract.