>>40853136Day of the week and time of day are both related to time, but they generally serve different functions, with one affecting Pokémon mechanics and the other affecting overworld mechanics.
Time of day: Visual distinctions between morning, day, and night. Different Pokémon appear at different times, like Ledyba in the morning or Hoothoot at night. Other Pokémon like Espeon and Umbreon have their evolution determined by the time.
Day of the week: No drastic visual distinctions, but usually things change in the overworld, such as which haircut brother is present, which day of the week sibling appears, the Sunday sale at the Goldenrod Department Store, whether or not you can access the area surrounding the Lake of Rage, Lapras appearing as an overworld encounter on Fridays in Union Cave, etc.
Ruby and Sapphire did have the time of day, but it was scaled back. There were no longer any visual distinctions for the time, the only way to check it was the clock in your room, no encounters were affected by it, the only two evolutions that were affected by it (Espeon and Umbreon) are completely absent unless you trade the already-evolved ones from Colosseum or an Eevee from FRLG where time isn't present. The only mechanics that do use time are Shoal Cave, the Mossdeep Space Center counting rocket launches, and berry growth taking place over a set amount of real-life hours.