Day/night are based on the player's local time. The morning starts at 4 am, day at 6 am, dusk at 6 pm, and night at 8 pm (these may be off by an hour if your region has daylight savings).

The maps reset at 4 am each day. This means that there's usually a limited number of a specific fish or item you can catch in a single day, and these reset at 4 am.