In this context it means that there is a basic difference. We can even say that there is a difference in the essence of two words. Perhaps an example would be the best way to illustrate this.
A desk is fundamentally different than a piece of metal. There is nothing that is similar.
Here is another example, but a more abstract one. Infatution is fundamentally different than love. Infatuation is really selfish and it is about how you feel, love is robust and uncondition, no matter what you feel. We can say that there is a fundamental difference.