The basic difference between “regular” thoughts and OCD thoughts are that OCD thoughts are unwanted and seen as inappropriate.
In addition, they cause significant anxiety and distress. Non-OCD thoughts rarely cause these results.
At times, some people may experience thoughts that meet a part of the obsession definition, but that does not necessarily mean that they have OCD. If a person has suicidal thoughts, he or she may see those thoughts as unwanted and inappropriate and be very distressed by them. But these are not necessarily OCD thoughts.
To diagnose a person with OCD, professionals will also look to see that the thoughts are not about real life problems, that the person tries to somehow suppress or neutralize the thoughts, and that the person recognizes that the thoughts are a product of his or her own mind. If the suicidal thought is a response to a difficult situation, then it is a concern about a real life problem, so it is not OCD.
However, some people have intrusive suicidal thoughts that are not related to any real life problems. They may try to suppress or neutralize them, and they may recognize that the thoughts are a product of their own mind.
In this situation, OCD could be diagnosed, given that all four criteria for an obsession are met.