There has been a great deal of research on the effects of individual differences on the perception of stressors and the experience of stress over the past decade. This has taken two main forms: medical and scientific research into why some people develop pathological responses to stress while others do not, and therapeutic research into how best to treat individuals under stress.
In a 2017 article published in Current Opinion in Behavioral Sciences (attached below), Karl Ebner and Nicholas Singewald argue that individual differences in perception of and vulnerability to stress are explained by the functioning of stress-inhibitory neural pathways. The authors claim that certain "genetic, epigenetic and biochemical factors ... may drive maladaptive processes in these stress-inhibitory circuits," leading vulnerable subjects to respond to stress in a dysfunctional way. The findings cited in this article are highly technical, and are largely derived from animal studies. However, a few easily-understood factors which make individuals particularly susceptible to stress do emerge, such as heightened levels of anxiety, anhedonia, and submissiveness.
The psychological or therapeutic approach to individual differences has historically been to observe a dichotomy between "positive" and "negative" reactions of stress. Investigators and practitioners would note that one individual would see a situation as an opportunity for development, while another would regard the same situation as a stressor, and a cause for anxiety. While the current approach is to regard such responses as points on a continuum, rather than a simple dichotomy, certain personality traits are still identified as broadly adaptive or maladaptive. For instance, high self-esteem and effective early socialization are important factors in preventing a pathological response. Where these are well developed, the subject may not perceive stressors or experience stress at all. The current state of the field in this area is well summarized by Katharine Parkes and Emily L. Hughes in their article "Individual Differences in Coping with Stress" in The Wiley-Blackwell Encyclopedia of Personality and Individual Differences (abstract and link attached below).