Actually, my degree is Applied Chemistry and Chemical Engineering. I’m technically qualified as a chemist and a chemical engineer.
There’s a lot of crossover between engineering fields. For example, most engineers study fluid flow which has helped chemical engineers design pipes and factories, aeronautical engineers to launch planes, naval engineers to build ships that float in stormy weather and bio medical engineers to understand blood movement through the body.
A food engineer can come from various backgrounds but the engineering principles are largely the same in all industries. What changes is the application (food, oil, wind, blood, electricity)