My cruises on the Royal Princess were booked as 3 separate cruises HOWEVER there were several cruisers who were booked as one 14 day cruise for the last 10 day & 4 day portion that counted as one cruise. Everyone was treated the same in terms of options in Ft. Lauderdale at the beginning of the 4 day cruise. Everyone had to clear customs again in Ft. Lauderdale (which was done by a custom agent who boarded the ship) and everyone was given an In-transit card in case they wanted to disembark.
Many people were upset when they realized that some got credit for more than one cruise while others did not. In our case, we got the free 250 internet minutes for each 10 day cruise and 150 free internet minutes for the 4 day cruise.
It's all in how you booked it! I met numerous people who jumped on the 4 day cruise at the last minute with a special offer from Princess that was phenomenal!