two ships of Theseus

[gorzek]

I assume you know the Ship of Theseus thought experiment: if you replace the parts of a ship, one at a time, until all parts have been replaced... is it the same ship?
What if you do this but someone else takes the discarded parts and rebuilds the ship entirely out of those?
Which one is the real Ship of Theseus?
Are both? Neither?
This is not a very smart thought experiment, I am mostly being silly.