Is the next Buddha the same entity/being as the previous Buddha, or another discrete being who comes to the same realizations as the previous Buddha? I do not have a strong theoretical grasp of the concept of rebirth, so I am wondering:

Is each Buddha that has existed/will exist the same being, reincarnated? Or is each Buddha a totally unrelated person from the previous Buddhas and Buddhas to come, who just happens to realize all of the same truths that the previous Buddha realized?

Thank you
Next Buddha is a totally unrelated separate person to previous Buddha. He will realize the same truth as previous Buddha when his(previous Buddha) teachings are no longer among us. 

Once someone becomes Arahant, He will never be born again. The whole purpose of being Arahant is not to be born again.

How can previous Buddha can tell prophecy about next Buddha?

To be a Buddha, its saying we have to do lot of good Karma and endless sacrifices. Buddha can see someone's Karma and how these Karma going to effect them. Therefore, Buddha can see whose Karma is fulfilled to be next Buddha and when it happens. 

As become a Buddha is so difficult, it's only for great persons who has endless courage and such a kind heart for all beings to preach them Dharma and make them aware of Samsara.