The pump you buy from Toyota is Aisin.... It's even cast into the body of the pump. A lot of Toyota's components come from them. It just happens that the one you get from the dealer also has "Toyota" cast into it. BUT you can also buy the Aisin pump without the "Toyota" label on it from third parties; It's the same pump just not paying that extra money for the name.
The GTE pump will fit the GE, the housings are the same and so are the pickups, just the internals vary. If building with slack clearances the GTE is definitely the way to go, the same if you've added more resistance to the system (ie: an oil cooler or remote filter mount).