My rule of thumb is to think about the processes and whether I could do them in my kitchen or not. Things like 'boil' or 'grate' are recognizable processes that I don't worry about. Thinks like 'hydrogenated' are indicators that some serious modification of the underlying ingredients has taken place.

The term 'hyper-processed' is used to refer to foods that bare very little resemblance to recognizable ingredients straight from the farm.