Are intrusive thoughts and unwanted thoughts the same thing or are they different?

Yes: I believe so, as intrusive thoughts are unwanted and unwanted thoughts are intrusive. These are not unusual but become a problem when too frequent. While doctors may prescribe pharmaceuticals for this, I advise a good multivitamin that contains L-5-methyltetrahydrofolate and also practicing meditation to learn how to control your thoughts (see videos on youtube). Also consider psychotherapy.