There are two main stress homones, the glucocorticoids (called corticosterone in animals and cortisol in humans) and the catecholamines (epinephrine and norepinephrine).
Corticosteron a natural corticoid with moderate glucocorticoid activity, some mineralocorticoid activity, and actions similar to cortisol except that it is not antiinflammatory.
Stress response involves the activation of the HPA (Hypothalamic-Pituitary-Adrenal) axis that leads to the release of ACTH by the anterior pituitary gland in blood, which in turn results in in the release of glucocorticoids by the adrenal glands. These glucocorticoids mediating the stress response are constitued by cortisol molecules in almost species (e.g. mammals, fish,...) while they are corticosterone molecules in rodents and birds. The chemical nature of the glucocorticoid is "just" species/order dependant.
Corticosterone is biosynthesized from progesterone via 11-deoxyprogesterone by enzymes CYP11B1 or CYP11B2. On the other hand, cortisol is biosynthesized by CYP11B1 via 17α-hydroxyprogesterone. In rats, mice, rabbits, birds, amphibians, reptiles, etc., they have little CYP11B1, so corticosterone is the only glucocorticoid in their circulation. On the other hand, in dogs, cats, primates including humans, etc. cortisol is the main glucocorticoid because of high activity of CYP11B1. By the way, mineralocorticoid aldosterone is biosynthesized from corticosterone.
Sorry, that's my knowledge for lectures of "Animal Physiology". Now, no reference I have. Maybe you can find anywhere in text books of animal physiology.
Because each of them becomes more concentrated in these species when exposed to stress and thus to know whether individuals have been subjected to stress, whether humans or rodents can be confirmed by measuring their concentration in the body.