Hyperdrives actually send ships into another dimension called hyperspace. Beyond that, scientists don't really understand very well how the drives work since the original hyperdrives were reverse engineered from Rakatan technology.
or what he said. Hyperdrives use Gamma radiation (If memory serves) to propel the ship into "Hyperspace" (the dimension Leo mentioned via essentially a man made Wormhole caused by the rippling of Space-Time) where it's able to travel at FTL (faster than light) speeds until you reach your destination in Realspace.
Warp drive (used in ST now SW mostly) works on the property that the drive "Warps" space-time, essentially co reacting the space in front of the ship and expanding it behind it, but the ship doesn't truly move, space does. Think of it like this, draw a circle on the top of a piece of paper, then scrunch the paper so there's a hump in the middle until the circle reaches you, now hold down on the circle and let the paper flatten again. Kind of like that (if I'm wrong, feel free to correct me)
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