Stress caused by trauma is by definition post-traumatic stress. It is commonly associated with war, car crashes or other violence but bear in mind that trauma is fairly subjective.
Not so. Traumatic events can cause an acute stress disorder that begins immediately after the event, while post-traumatic stress disorder by definition has a latency of at least six months.
Yes, but to be a disorder it has to meet specific criteria.
Specific criteria set out by the DSM, the most recent version of which is essentially a checklist of symptoms for doctors to classify mental health on behalf of insurance companies for billing and labeling purposes. As a layperson, undiagnosed and untreated for any 'mental illness', and in my personal opinion, every new edition of this 'psychologists bible' demonstrates to me the entire point is quickly getting lost, and serves a different master than the wellbeing of patients. Its confirmation bias for my decision to go into technology rather than psychology, so take this with a grain of salt.