One of the most important aspects of what separates harmless stress from the stress that makes you ill is duration. We can cope with a brief period of stress, so long as it isn't too traumatic or overwhelming. The problems arise when we stay stressed for long periods of time, because it's not what we're designed for. We are designed for life on the primordial plane millions of years ago. Natural selection adapted us very well for that environment. Our basic design hasn't moved on a lot since then because few things in our present lives threaten our ability to make it to child-bearing age. In those days life was mostly very dull, interspersed occasionally by short periods of extreme danger or opportunity. If an antelope passes your cave, you've got about 20 seconds to do something about it, or you and your family won't eat for a week. If, on the other hand, you emerge from your cave to be confronted by a sabre-tooth tiger, what you do over the next 20 seconds will determine whether you pass on your genes or not. So we got very good at dealing with short periods of stress. The hormone adrenaline was evolved to cause a range of changes to the body to occur very quickly when the need arises. It does a brilliant job, turning us into finely adapted machines able to fight or to run at the peak of our body's capacity.
Within a few heartbeats, adrenaline, released by the body in response to perceived threat, affects almost every bodily function. The heart beats faster, to pump more blood around the body, we become breathless so as to load up with more oxygen, the blood vessels to the muscles and the skin dilate, to allow greater muscular activity and to lose heat, which we are sure to generate in our flight from the beast that is chasing us and all our nerves become super-sensitive as we are going to need all possible acuity in the life or death struggle ahead. In addition, the bowels will tend to open up at both ends, as this can allow a rapid jettisoning of a few pounds of body weight, helpful in running faster and will lay a powerful scent trail. As most of our predators in those days relied heavily on their sense of smell, while we don't, the confusion that this causes gives us a few seconds to find a crevice to crawl into to avoid being eaten.
All highly adaptive if you're being pursued by a sabre-tooth tiger, but little use to you if you're sitting in an office, or a restaurant, or at home.
So adrenaline makes us well-adapted to short-term stresses. The problem is that that isn't the way our modern world is constructed. There are few wild animals threatening to eat us and most short-term threats to life and limb have been eradicated. The threats we face are more subtle, more subjective and much longer lasting. We aren't designed for that. So we suffer the effects of stress, rather than being enhanced by them and the same heightened arousal that protected our ancestors makes us ill. Natural selection doesn't care. Most of the physical effects of chronic stress don't threaten our lives until after the normal reproductive years, and as far as natural selection is concerned we are, by then, disposable.