I'm especially curious about the steam ships carrying emigrants over the Atlantic, as I thought of this question after visiting an exhibition about Titanic. She struck the iceberg "at 23:40", and Wikipedia further elaborates that this is what the ship's own clocks were set to. I also found a thread on AskHistorians with a reference to "ship time".

I'm assuming it was solar time to some degree of accuracy. How often were a ship's clocks set? How were scheduled events like dinner services timed? Did they start using time zones at any point after GMT and US railroad time were somewhat standardized? Was travel before steam power slow enough that timekeeping was only a concern for navigation? I'd appreciate answers to these or any other related question you can think of.