A Remanufactured engine is the best way to go when New is not an option. The Engine is completely disassembled and all components are machined so that all surfaces are fresh. All bearings are replaced. New oil pump, New rings, Fresh Valve Job and or New valves as needed. Cylinders are Bored and Honed. Connecting rods are machined. Generally has the best warranty available.
A rebuilt engine is merely disassembled, cleaned and any component that has failed it replaced or fixed. Then the engine is put back together with new gaskets. What this means is that if the only problem was a cracked head, the head was repaired and none of the rest of the components were touched. And if you had your engine rebuilt, in most cases the warranty will only cover the part that was replaced and not the rest of the engine.
If available a new engine can be the best way to go. New means New, This engine has not been in any vehicle ever. This engine has been manufactured from scratch and has zero miles on all the components.
The difference between a Long block and a short block is pretty simple. The Long block comes with heads and valve train. The Short block does not.