There's no one-size-fits-all answer to this question. Experiences varied widely between ships. While larger ships generally hewed closer to a strict system and smaller ships were more casual, there were always exceptions. Men who worked on the bridge would have more interactions with the captain than those who worked in the engine room. This answer will focus on the Royal Navy in WWII, but should not be taken to be universal.

On larger ships (capital ships, carriers and cruisers), the captain was generally insulated from the crew by the rank structure. In the Royal Navy, the captain's job was to command the ship; the crew was commanded by the commander (executive officer in USN parlance). It was the commander's job to organise the crew, and to look after discipline. The commander was expected to supervise the crew's work, and as such, he would be very familiar to the crew. The captain, meanwhile, was a more distant figure. He was still expected to know the names of the crew, and to maintain close links with senior NCOs, but would not be part of the typical crewman's life on a daily basis. The two would only come into close contact on special occasions. The captain would run a periodical 'requestmen and defaulters' session. This allowed men to make requests of the captain (for example, requests for transfers, leave or promotion), and also for the captain to hand out punishment to defaulters. The captain was the only officer able to hand out the more serious punishments like imprisonment, while the commander could only sentence men to extra duty and drill. The captain would typically hold an inspection every Sunday. The crew would be drawn up by divisions on the deck for the inspection, during which the captain might well question members of the crew about their life and duties. Following this inspection, the captain would participate in the ships' church service, reading out a lesson from the Bible. The captain was also responsible for giving the service for burial at sea.

Other special occasions would upset the rank structure. When a ship crossed the equator, a 'crossing the line' ceremony was held. During this, the officers lost their authority. Instead, it was held by a member of the crew dressed as 'King Neptune', who would hand out ritual humiliations to all aboard who had not previously crossed the equator. At Christmas, it was not uncommon for the most junior member of the crew to be declared captain for the day. While he had no real authority, he was given many of the privileges of the rank.

Smaller ships tended to be less formal. While they did have an executive officer, the first lieutenant, the lower numbers of officers aboard meant that it was hard to keep up the strict systems seen aboard larger ships. Inspections were rarer, but other systems prevailed. On larger ships, the captain ate alone, on smaller ships, he was part of the ship's wardroom, eating with the other officers. Captains tended to overlook minor infractions in things like dress, encouraging closeness between them and the enlisted men. On smaller ships, the captain was more involved in the day-to-day running of the ship. This brought him into contact with more of the crew. As with large ships, captains were expected to know their entire crew. This was considerably easier on smaller ships, with a smaller crew that the captain was in greater contact with.