No, only people with OCD have obsessive thoughts.
However, everybody does have intrusive thoughts, or thoughts that randomly pop into their head. Most people are able to shrug them off, but people with OCD do not.
Instead, they attempt to ignore, suppress, or somehow neutralize the thoughts. They may tell themselves to never think that thought again, or they may attempt to replace the “bad” thought with a “good” thought.
These activities are the beginnings of obsessive thinking.
The more that thought suppression or neutralization is attempted, the more likely the person will develop OCD.