Retelling is taking the story, keeping it's heart, but changing the details to suit the new audience.
Ultimate Spider-Man was still recognizable as Spider-Man, but he worked for the Daily Bugle as a web designer rather than a photographer, MJ was his friend right from the beginning, and his origin as Spider-Man was tied into Oscorp and the metahuman arms race.
Ultimate Thor wasn't that different that 616 Thor. For the first few years of Thor comics, Thor was just a man named Donald Blake who found the enchanted walking stick that gave him Thor's powers. Then later on Odin revealed to him that he actually WAS Thor, but that he had been stripped of his powers and memories so he could learn compassion and responsibility and become worthy of his power. The Ultimates took that concept and ran with it. They made us wonder if Thor was just a man with incredible powers, or really Thor. If a Norse god showed up today, what would he be like? How would people react to him? Would we believe him?
Rehashing is telling all the old 616 stories again "ultimate style." Ultimate Dark Phoenix, Ultimate Thanos, Ultimate Diablo. This was when the Ultimate line started to decline. Nothing felt fresh any more because they were just taking known stories and rewriting them. So they tried to make it fresh again by drowning everyone.