I think emotions are more a philosophical matter while stress is more medical. Stress in general is a heightened state with respect to a basal rest state. It’s mentioned a lot nowadays but I think it’s too unspecific to be useful as it doesn’t allow for much introspection. Emotions can be dissected, felt, recalled, and analyzed by oneself.

As I understand it, emotions are a representation of a train of thought which may or may not then cause physiological effects. If I’m watching a sad movie, feeling the emotion of sadness may not stress me. It may actually be exhilarating because it’s allowed me to feel an emotion that I hadn’t felt in some time. Stress on the other hand is by definition an effect which may have many causes. Think stress of materials. An emotion may be one but also trauma or even a tumor.

I can reach those values by exercising or even constricting muscles (e.g. sphincter) but you wouldn’t say that I’m stressed. Stress as I understand it is a complex state characterized by among others, excess anxiety, increased basal metabolic rate, heightened awareness. Essentially an increase in most dimensions from a basal rest state.