Transfers
You can freely move ships around between I-Ships, P-Ships, and all the fleets that are present at a world at the beginning of a turn. This is called a transfer.
Transfers take place after unloading metal, and before loading more metal. If you transfer ships that are carrying metal without unloading the metal first, the metal will not transfer and may be lost.
Transferring ships to a fleet does not capture the fleet. Instead, transferring ships to a fleet you don't own will just give the ships away. Sometimes you want to do this (for instance, to give ships to an ally). If you transfer ships to an unowned, empty fleet key, you will create a neutral fleet, which is almost always a mistake.