In the clinical definition, PTSD is a psychological disorder that develops in some people after a trauma. Interestingly, not every traumatized person develops chronic (ongoing) or acute (short-term) PTSD, nor has every person who develops PTSD gone through a dangerous event. The 'trauma' in the name can refer to events as diverse as hearing about a traumatic event from another person or seeing it on TV, or the death of a loved one (even if you weren't there).
The most important parts of diagnosing any mental illness are (a) is it causing suffering (either to the patient or other people), (b) it is statistically significant (is it unusual for the culture of the patient).
In the case of PTSD, it is enough that they are suffering for the clinician to look further.
PTSD usually occurs within 3 months of the incident, but some people develop symptoms after more than a year. Most people recover within 6 months, but others have long-term chronic symptoms.
To be diagnosed, a patient must have a constellation of varied symptoms. The ICD-10 and the DSM-5 describe the most common diagnostic criteria used today.
The best plan for a clinician is generally to develop a holistic outlook that takes into account the dynamics of the patient's case rather than to try to pigeonhole the patient into diagnostic criteria. Someone who experienced a traumatic event and has residual anxiety and depression may or may not be diagnostic with PTSD. PTSD, under the DSM-5 criteria, must include one re-experiencing symptom, one avoidance symptom, two arousal and reactivity symptoms, and two cognition and mood symptoms.
Since the treatment most commonly indicated for PTSD is anti-depressants/sleep aids and psychotherapy, which are also the treatments for many other mental illnesses, the particular diagnosis is less important than the welfare of the patient. PTSD patients can also benefit from exposure therapy and cognitive restructuring.
The US National Institute of Mental Health has a good introductory article on the subject.