Well, Clawtius, I never thought you were wrong. Of course both answers were correct. Tolkien had multiple names for just about everything.
Lots of spoilers:
I do not recall Olorin being reluctant to go, but perhaps I have not read that part yet. Saruman is an ancient being, and his insecurity is almost endless, particularly in the absence of the mighty Valar, with whom he can be comfortable being inferior because it is not close. But being one of only a half dozen Maiar in Middle Earth, perhaps part of his motivation was proving himself.
I don’t recall Gandalf ever saying he feared Sauron personally, or other than what evil Sauron might do to the world. He fears what he would become if he had the ring, but Sauron ain’t gonna tempt him or anyone else with that. Personally, Gandalf is bizarrely fearless, considering just how weak a Maia he is. This is no Osse or Melian. He stays and fights the Balrog because he knows that he can keep it from crossing the bridge before he dies. And he is not afraid of death, but perhaps his own corruption.
Gandalf the White, however, is sent back with far greater powers. He can see Sauron and strive with him over a great distance. He can see events from afar. Particularly in TT (I just reread LOTR), he is supremely confident in his abilities, a sharp contrast to his pre-death experience. This wans a bit in ROTK, probably for dramatic plot reasons. While Saruman was able to beat Gandalf in a wizards duel in FOTR, Gandalf dispatchs Saruman with just his voice in TT. His voice alone forces Saruman to the railing, his voice alone breaks Saruman’s staff. Now perhaps the Istari are limited from using the Maiar powers by their human form, but this suggests an enormous increase in power. It tired Gandalf to speak with the word of command at the chamber of Marzabul and to strive with the balrog to hold the command, which was rendered moot by the very rock breaking. His greatest feat of magic was the all out lightening attack (alluded to only) when facing down all the Nazgul at once on Weathertop. And he was forced to flee IIRC.
The balrog only stopped temporarily at Gandalf’s command at the bridge. It was of no use with Saruman in the first battle. Gandalf didn’t even try it on the Necromancer (Sauron) at Dol Goldur when Sauron was still weak. One gets the sense that he was sent back with instructions to let the mortals use their own gifts (with encouragement only) to defeat Sauron or be defeated, but that he could command Saruman to be defeated to do housecleaning. The only similar battles in Middle Earth are between Finrod Felagund and Sauron and Luthien and Sauron, both of whom Sauron defeated. And ordinarily the powerful Elvish princes could defeat a balrog (a form of Maia) in single combat. These were both battles of song IIRC. Luthien, in fact, defeats Morgoth with a song battle, rendering him completely helpless.
While Gandalf was not the kind of “high voltage” powerful, he was powerful in his perseverance and his knowledge of himself and other beings. He uses this knowledge to great advantage.