"It is now during the first ten days of the tenth month in the twentieth year of Kanei [...] The time is the night of the tenth day of the tenth month, at the hour of the tiger."
-Miyamoto Musashi, The Book of Five Rings, Introduction
As I write this, by Musashi's reckoning it would be the third year of Reiwa, at the hour of the sheep. But to you and I, it's roughly 2 PM in 2021.
Different cultures mark time in different ways. Ours, in particular, is one of the relics of the old Roman empire, dating back to 700 BC. Well, mostly. It's been revised a few times, but the Republican calendar has 12 months and you can probably figure out what "Mensis October" correlates to in the modern Gregorian calendar.
But the weeks of the Roman Republican calendar are eight days each. (Except for winter! Winter wasn't organized into weeks. Cool!) The seven day week you and I are familiar with dates back to the Babylonians and was popularized in Judea, and we see it prominently in the Bible.
Other week-lengths are found in some cultures: Six days in the system of the Akan of West Africa, five in the 10th century Icelandic calendar, and even three for the Guipuscoan Basque of Spain. Between 1793 and 1902, France ran on 10-day weeks.
The names of our months and days carry cultural influence as well! January, the month of Janus, Roman deity of beginnings, time, doorways, etc. Thursday, the day of Thor, you know, from those Marvel movies. (Sidenote: Thursday in most of the Romance languages has a name derived from Jupiter. Jueves, jeudi, joi, etc.)
What I'm getting at here is that our system of weeks, months and (the names of) days isn't an absolute fact of nature. It's heavily influenced by our history and our culture. And the calendar of your fantasy world probably is, too.
Maybe your fantasy world runs on a seasonal calendar. Just four "months," or however many seasons your world has. I don't know, maybe there's one where it rains squid all month. It's your world. Go nuts.
Maybe all the months are named for old emperors or deities, modern or ancient. What superstitions could there be about a month named for a now-dead god?
Are the years named for rulers? Generational cycles? Are they assigned names at the end, like the Year of Frost, the Year of Deathly War?
Note, as well, that these systems may not be consistent between cultural groupings. Perhaps the elves reckon time by seasons without months. And what of the dwarves, forever underground? How do they mark the passing of time?
One important thing before we get into the examples: Calendars are based on cyclic phenomena. Orbits of the planet, the cycles of the moon, etc. If a volcano erupts every year without fail, or an angel appears at a regular interval to chide the unworthy of the capital city, those things may also make a suitable basis for time-keeping.
Here's an example: You've got your fantasy world with all the standard races. For simplicity, let's say the year on this world has 400 days.
Elves split that into four even seasons: Spring, Summer, Autumn and Winter. 100 days each. Weeks hold no importance for them, as they hold no importance for foxes or ferns. The closest they get to phrases like "next week" is "in a tenday" and the like, meaning ten-ish days from now. Some particular subsets of elves may use fancier titles for the seasons— The Time of Growing, The Time of Thriving, The Time of Remembrance, The Time of Hardship— but the basic structure is used by most elven groups.
The Dwarves, at the far end of the spectrum, don't count months at all. For them, the year consists of 66 weeks, each of which is named for a particular hero, gem or metal. The Week of Sapphire, followed by the Week of Steel, followed by the Week of Madbeard the Lad. This is one of the more confusing aspects of dwarven society for outsiders. If you've been doing the math as you read along, you may have noticed that that leaves us with four days to spare. Never fear! Those four days aren't part of any week, and are set aside for a few days of feasting, drinking and reckless merriment in the depth of winter.
Humanity uses 10 months of 40 days, split into 7 day weeks that do not line up nicely in any way, and frustrates the orderly dwarves. Their months are almost all named after deities (Bahamutia, Iona, Heironeus, Gruumshia, Quartober [Latin for fourth month, roughly. Ask a scholar why it's the fifth month some time, ideally when you've got a whole day free.] Cuthtober, Moradina, Kordis and Festa, the month of festivals.)
Goblins mark the days by which constellations are visible at night. Several books have been written by human and dwarven scholars on the exact mechanics of this, but according to goblin liaisons, "you just get the hang of it at some point."
Now, let's look at the sci-fi side of things. Will the humans of the year 3000 still use AD/BC? Maybe. Maybe we use the Chinese calendar, or the Hebrew calendar. Barring those, a popular option is to "zero the calendar" at some important event. Maybe time is counted since what we would call the 12th of April, 1961, the day the first human went to space, which would make the year 3000 the year SA 1039. In a more dire future, maybe humanity marks time since the destruction of Earth.
The most likely scenario for a space-faring humanity is probably to treat every space craft like it's at one particular point on Earth, or some future capital world. Depending on the rigidity of the society, this may break down once you land on a planet, which may have its own calendar based in its actual year and day cycles.
In a more fantastic setting, perhaps years are marked by the movements and mating cycles of some interstellar fauna. Perhaps the new year is when the Space Trout warp back to the Spawning Grounds.
Maybe they don't bother with years or months or weeks at all, and use something like Star Trek's Stardate system, which I will not pretend to understand. After all, what significance does the rotation of some rock hold to a space-faring race?
I'd like to end this with one final note: Your players might not care. You should probably figure out if they will before you spend a ton of time figuring out how every culture marks time.