Well, the original pyramids were more like 'High Rise Mastaba', multiple tombs stacked on top of each other, it was probably this that gave them the idea, much as the Mayans did, though I don't think the 2 sets of pyramids are related in any way, it's just an obvious conclusion to jump to. The further lack of relationship is displayed by how the builders refined their designs. Egypt plated their pyramids with smooth limestone, which must have looked utterly incredible when they were new, since Limestone can act like a mirror in the right conditions in the Desert (Which further suggests that they were a monument to Ra, since they would would have been blindingly bright in full sunlight). The Mayans enhanced the 'Step' technique, building some incredibly complex tombs.
It's like the belief that Egypt was a 'Death Culture', it wasn't. They just had a LOT of room to build their mausoleums in. And a lot of Rock to build them with. They revered the dead, but thats the only point in which Egyptian and Mayan death culture even get close. No form of Egyptian magic ever suggested it was possible for Mummies to come alive, and, despite common belief, the 'Curse of Tutankhamun' is very much a matter of debate because of the wording of the 'Curse'.