I think we can say that Paradise is an actual place, and Heaven is more of a concept.
The Urantia Book refers to God many, many times as the "heavenly Father," or the "Father in Heaven," but my feeling is that they use that term as a concession to humans' ideas that are age-old - such as the term "heaven," which is a very traditional idea that probably all people are familiar with. I think this is likewise true of the term "Kingdom of Heaven." They also refer to "the heavens," which seems to me to be a general term that covers the cosmos - the stars, galaxies, universes, etc, even though all of the stars and heavenly bodies are known and named somewhere. For us, they use the catchword "heavens."
Again, when most people hear these words, they likely think of a place of peace, happiness, joy, and they think of it as the place they will go after death. We know from Urantia Book revelation that we actually go to Mansion Worlds, Jerusem, Edentia, etc...again, actual places. I am sure that our experiences even on Mansion World One will far outshine anything we might have imagined that heaven will be like. But the revelators call Jerusem our "first heaven.":
47:10.2 John the Revelator saw a vision of the arrival of a class of advancing mortals from the seventh mansion world to their first heaven, the glories of Jerusem. He recorded: "And I saw as it were a sea of glass mingled with fire; and those who had gained the victory over the beast that was originally in them and over the image that persisted through the mansion worlds and finally over the last mark and trace, standing on the sea of glass, having the harps of God, and singing the song of deliverance from mortal fear and death." (Perfected space communication is to be had on all these worlds; and your anywhere reception of such communications is made possible by carrying the "harp of God," a morontia contrivance compensating for the inability to directly adjust the immature morontia sensory mechanism to the reception of space communications.)
On the other hand, the authors introduce us to Paradise as a very distinct place, and then they go on to reveal exquisite details about Paradise, the dwelling place of God:
"Paradise is the eternal center of the universe of universes and the abiding place of the Universal Father, the Eternal Son, the Infinite Spirit, and their divine co-ordinates and associates. This central Isle is the most gigantic organized body of cosmic reality in all the master universe. Paradise is a material sphere as well as a spiritual abode. All of the intelligent creation of the Universal Father is domiciled on material abodes; hence must the absolute controlling center also be material, literal. And again it should be reiterated that spirit things and spiritual beings are real."
And of course, Paradise is also our ultimate destination after the adventure of mortal ascension.
There is nowhere in The Urantia Book that describes any specific place called "heaven," so I think that the difference between them is the difference between an idea (heaven) and a reality (Paradise).
Thanks so much for this very good question!