My dad was a harbor pilot in Alaska for 30 years (he retired a few years ago), and loved his job. It is very challenging (especially in Alaska).
It is true that it is a federal law that a pilot is on board as the ship comes into port and leaves port, and there is a "pilot station" about 2 miles outside of port where the pilot boards (sometimes they just get on the ship via a small door on the side of the ship, like on cruise ship, sometimes they climb up a ladder up the side of the ship (this is the case for most non-passenger vessels, and the super tankers, which are huge, are quite a climb, and then add in the bad rough weather... it takes skill!).
Yes, all Capt_BJ wrote is right on! My dad has had situations where he takes control from the moment he gets to the bridge, because that is what the captain wants, and other situations where the captain wants to do it all, and my dad doesn't do much. And, my dad got to know many captains over time, so before he even boarded a ship, often he would already know who the captain was, and this helped him know what to expect once getting on the bridge. But, that is a good way to describe it that there is "a little dance" to set boundaries... very true.
In Alaska, the pilot often will stay on board for 3 days straight as there are so many narrow channels, tough currents, extreme tides, etc. (in this case, there are two pilots on board, and they relieve each other so the other can sleep... this way, there is a pilot on the bridge the entire time). And, there were times where my dad and the captain (a.k.a, "the old man" ... slang term for captain) would disagree on the approach my dad would be advising, and there wouldn't be much time to work out the disagreement, and there have been times my dad has just overridden the captain because my dad was the expert in the water ways/ports, and he knew if they did things the way the captain was wanting, it could mean bad news. But, that doesn't happen often... most of the time, they work together, and listen to each other's advice... But, it's true, every job is so different, depending on the ship, the captain, the weather, the port... so many factors.
And, yes, it's usually the 1st mate who actually steers the ship... the captain nor pilot does that... except, yes, with the remote control controls, the captain or pilot will run those, but on the bridge itself, the captain or pilot just gives orders to the 1st mate.
I got to go with my dad on many of his jobs (pre-9/11), and it was always fun to see all the action unfold on the bridge.
I loved my dad's job... it was so unique and interesting!
My dad always brought home lots of great stories!
My favorite "cruise ship" storie from my dad is it was pretty rough seas when the pilot boat came along side the ship to let my dad (plus another pilot who was boarding with him). When the pilot boat comes along side to let the pilot(s) off onto the ship, if there are rough seas, they try to time it just right with the waves where the pilot jumps from the boat to the ship right when the pilot boat is even with the door to the ship, before the pilot boat drops down from the wave making it uneven.
Well, in Alaska, the pilots are required to wear suits and ties on the bridge (at least the SouthWest pilots were required to... not sure about SouthEast pilots), and my dad and the other pilot went to jump on the ship when it seemed to be timed right with the waves, and right at that moment, a big wave splashed on both of them drenching them completely from the waist down! Well, they had to make their way up to the bridge (drenched from the waist down, dressed in suits, so passengers would have though they were a passenger). They just took the stairs all the way up (I forget which cruise line it was), and my dad said they got some pretty strange looks... LOL!! Luckily, they had changes of clothes with them (since it was a multiple day job), so they were able to put dry clothes on. But, I'll never forget that story. I can only imagine if you were a passenger seeing two men dressed in suits and ties walking up the stairs totally drenched from the waist down how perplexing that would be! LOL!!