I hate the term 'stress leave'. It's sick leave. Physical or mental, an illness precludes you from being able to work. Full disclosure: I burned out hard this time last year and was off for four weeks for exactly this reason, and I'm currently walking on eggshells to avoid it happening again.
To go off on sick leave that would be characterized as 'stress leave', you're getting an opinion from a licensed medical clinician that you're ill, and that for that reason you cannot presently work. Depending on the organization in question, there will be a variety of different configuration of short terma nd long term benefits for illness. In CAF and the RCMP, you simply have indeterminate sick leave while your case is managed by the respective organization's health services, and you potentially end up on a permanent medical category with restrictions, or wholly unfit for further service and you transition out. Other emergency services employers will have some sort of short term sick leave, and then you generally transition to a private insurance company that has some sort of long term disability plan. If you can't come back to your substantive job within a couple years, the goal shift to can you be gainfully employable at all, and you have to work towards that to protect your income replacement benefits. Or, if it's work related you might fall under worker's comp.
As to where this degree of stress comes from? It can be anything from single acute or repeated chronic traumatic exposure, to long term overwork, harassment in the workplace, or reasons wholly unrelated to work.
Fundamentally, this comes down to the rights under human rights legislation to not be discriminated against on the grounds of disability. Anxiety, depression, PTSD or what have you are disabilities, and employers have the duty to accommodate same to the point of undue hardship. Coverage under sick leave and long term disability simply makes sense; those are all set up to try to facilitate the successful recovery of the employee and their eventual return to the workplace.