I guess there are degrees of intrusive thoughts, because no, it’s not really the same. ‘Don’t think about the elephant’ causes a benign and very fleeting fixation.
Intrusive thoughts are things that linger, often in a disturbing way, long after you want them gone. They interfere with your ability to focus.
The elephant thing is like a musical ear worm whereas intrusive thoughts can be like someone blaring industrial music in your ears. I’m not explaining this well, but it’s on another level.