It's time to get all northern European with this question about Norse cosmology: Hey guys, sorry to bother, but I have been wondering, is there any relation between Mani and Nott? Also between Sol and Dagr? They seem to do the same thing, or am I missing something?
They're definitely separate figures with different functions, but I can see where you could get understandably confused! Mani is the Norse personification of the moon, accompanied by his sister Sol, the personification of the sun; conversely, Nott is the primordial goddess of night, and Dagr the god of the day. The moon and sun certainly appear during the night and day respectively, but they're just a part of what makes up either period of time, and have their own gods just as those concepts do in other mythologies. For example, in Egypt, Nut is the goddess of night but there are several discrete gods of the moon, including Thoth and Iah, who are obviously separate deities, and likewise in Greek mythology there are separate deities for the day itself (Hemera, ancient personification of daytime) and the sun that rises during it (Helios and Apollo, most notably).
Essentially, the answer is that the moon is part of the night and the sun part of the day, but that doesn't mean that they're the same thing, just that they're linked concepts with their own deities representing them. So, let's talk about these neat folks!
Norse mythology is cosmologically vague, like a lot of other ancient European religions; it tells us about several things that exist and what their names are, but seldom describes them in thorough detail or gives us much of an idea what those things might have meant to those people who believed in them during their heyday. Only a few lines from ancient Norse mythological sagas tell us about these deities, but even those few lines are enough to be evocative (and to spawn centuries of battles royale between disagreeing scholars. Northern European mythological studies is a shark tank).
Dagr appears in the Sigrdrifumal portion of the Poetic Edda, wherein the valkyrie Sigrdrifa prays to him along with several other deities and hails him as the father of many sons, and also in Vafthrudnismal, where he is mentioned only in passing as the son of Delling, the personified god of the dawn. The Prose Edda expands on him by confirming Delling as his father and Nott as his mother, and describes him as radiant and fair like the rest of the Aesir; it also explains that Odin gave to Dagr a horse named Skinfaxi ("shining mane"), so that he can ride the horse around the sky every day and illuminate the world with its bright and golden mane.
Theories abound when it comes to trying to connect other Norse stories to Dagr, with the most popular being the idea that the famous Norse hero Svipdagr ("sudden day") is actually the same god, and his adventures in Svipdagsmal actually stories of his interactions with several of the other Aesir including Odin and Freyja.
As in many other cultures, Dagr as the day-god has the important job of constantly traveling the skies to make sure that there is light during the day. This is where it's easy to wonder if Dagr might be the same as Sol, because she, too, performs this sky-chariot job - but she's a completely different deity with different character, described separately in the same texts.
Sol's name means literally "sun", and she is the daughter of an enigmatic god named Mundilfari, possibly a deity of time and seasons (which would make sense since his children are the moon and sun!). Sol appears in the Poetic Edda as well, where she is described as not knowing where her home is in the disorder at the beginning the universe, which causes her to wander without any guidance until time is eventually set in order. Her travels, along with Mani's, are said to help provide humanity with the means to measure time, and Odin mentions when describing her that she is constantly pursued by the terrible wolf Sköll, a child of Fenrir, and that he will catch her at Ragnarök and devour her, plunging the world into darkness. He also notes that she will give birth to a daughter just before she dies, however, who will take over as the new sun when the world is reborn after the battle.
Sol also appears in the Merseburg Incantation (where she's called "Sunna", from which we get our modern English word sun) performing healing charms over Baldr's horse as she travels with several of the other Aesir. And in the Prose Edda, she is given a backstory in which it is explained that she and Mani were so beautiful when they were born that they were named "sun" and "moon", but that the other gods considered this to be unforgivably prideful, so they were banished to the skies to actually fulfill the roles they were named for.
Her brother Mani (literally "moon", like all the other literal names on this list) shares most of the same information with her; he, too, keeps time for humanity by driving the moon across the sky in his chariot, was also exiled there for being too beautiful and prideful, and is also fleeing a wolf, the terrible Hati, who will devour him when the inevitable apocalypse comes. He controls the waxing and waning of the moon at will - interesting, since for many moon gods this is something that has to be explained by a separate myth - and is accompanied by two children, Hjuki and Bil, whom legend says he kidnapped from the earth while they were drawing water. No one is really sure exactly what's up with Hjuki and Bil; one theory suggests that they might be personifications of the spots visible on the moon's surface, while another suggests that they represent Mars and Venus, the brightest stars in the sky.
No mention is made of Mani having a son to take over for him as the moon when he dies, but most scholars guess that this is implied, since otherwise humanity would be ill-equipped to start over in the new, post-apocalypse world with only a sun to regulate their lives.
And then finally we come to Nott ("night"), the personification of the nighttime hours who shuts the world down for the evening as opposed to her son's time during the day. Nott and Delling together producing Dagr makes cosmological sense; night unites with dawn to give birth to day, a quick description of the progression of time over the course of the day. Nott rides Hrimfaxi ("frosty mane"), the magical horse given to her by Odin, and draws night across the sky with her as she goes, while the foam from the horse's exertions falls to the earth and becomes the dew that apears on the grass in the morning.
The dwarf Alviss gives "dream-goddess" as a kenning for her name, probably referring to her role as deity of the night again since sleep and dreams are usually the province of the night for humans. And although she's just as faraway and sparsely described as the other gods in this post, she is more closely linked to the rest of the Aesir by virtue of being the grandmother of Thor through her daughter Jord, the goddess of the earth.
So we definitely do have four different deities riding about the heavens doing celestial things, but they are all distinct and individual figures described at various times in Norse myth. This isn't uncommon in mythology, especially when older gods are replaced by newer more popular ones who do the same jobs, gods are borrowed or absorbed by other nearby people or they specialize in different niches within the same overall idea. But they have their own unique character, so don't be surprised to see one or more of them on your journeys!