The letter K went out of style and went out of style hard in the Latin alphabet. It was redundant since they had the letter C (always hard in Latin) and so when they transliterated kappa they did it not as K but instead as C.
So, people tend to confuse the two, and they have for a long time, and it's not just a question of spelling.
Chronos/Chronus is the god of time. He's not well preserved. You see, Chronos was part of the Orphic tradition. The Orphic tradition is pretty well fucked in terms of transmission.
As a result, Chronos/Chronus is very much bereft of a mythology. He created the world egg, unless he didn't, and . . . that's about it.
Kronos/Chronos/Chronus is the god of . . . nothing really. He is well preserved. He's part of the traditions that do get transmitted well-ish. There's really nothing where the transmission is good, but Greek Mythology is in many ways the best, and Kronos is a part of that. A part that didn't fall into the hole of, "Well, almost everything gets lost over time."
The story goes something like this:
After the creation of the universe Gaia and Ouranous/Uranus were lovers and Ouranous was, for unfathomable reasons (fuck you patriarchy), the one in charge.
He liked having sex with Gaia, but wasn't too big into the initial results. These were the Kyklopes/Cyclopes of old (not to be confused with the younger ones) and the hundred handed ones. Ouranous locked them away in Tartaros/Tartarus. This pissed Gaia off.
The Titans, not named that yet, on the other hand he was ok with.
Kronos was the youngest Titan and this was the situation he was born into. Eleven of his siblings (the other first generation Titans) were free, his eldest siblings were imprisoned, his father did the imprisoning, and his mother wanted it to stop.
When Gaia asked her free children to help her save her imprisoned ones by violently opposing Ouranous, only Kronos, the youngest, stepped up.
Kronos attacked his dad by chopping off his genitals, which seemed to have done the trick because after that Kronos was undisputed ruler.
Kronos was an asshole though. He reneged on his deal with his mother and left his siblings imprisoned. He, like is father before him, found them aesthetically displeasing and kind of scary.
Prophecy said that he'd be overthrown by one of his own kids, just as his father was overthrown by him. So he ate them.
When it got to the sixth child, though, his wife and his mother collaborated to save the kid, that being Zeus.
When Zeus had grown he began his fight against Kronos by inducing a vomiting fit which freed his older siblings. (When a god is eaten, the god doesn't die.)
Then Zeus set free the Kyklopes of old and the hundred handed ones, as Kronos had promised to do but never done.
Finally Zeus sent out a general call for anyone pissed off with Kronos to join him in the coming war.
Kronos based his side on Mount Othrys, Zeus chose Mount Olympus.
The war lasted ten years.
Kronos lost; he was imprisoned in Tartaros and the hundred handed ones made sure he stayed in the prison he refused to free them from after promising to do so.
The point here is that Chronos has purpose, he's the god of time, and Kronos has story, see above, and if you put the two together you get a god with purpose and story. So people did that. And people do that.
People have been doing it for over two thousand years. How far over? Not really sure. The Latin sources that conflate the two claim that the two have always been conflated but that seems questionable to me.
The takeaway should basically be this:
Chronos: God of time whose mythology we've almost entirely lost.
Kronos: God of [no clue] who plays a large and important role in the mythology we haven't lost. Father of Zeus and siblings, former king of the gods.
Don't worry if you get them confused, there's a long tradition of doing that, but it's best to at least try not to.
* That's not to say that we know nothing of it. There are ongoing attempts by brave scholars to reconstruct the beliefs and practices. I'm sure there are non scholars doing the same. And every so often we get our hands on a relevant papyrus. It's not like archaeology is done with.
So, if you think that Orphic paganism is the path for you, there are resources you can draw on. And, mostly, I don't want to make it sound like Orphism is dead. I very much doubt it is. This is a religion whose founding prophet was a poet extraordinaire and the best musician ever, whose lyre performance was more powerful than siren song and allowed be used to walk into and out of the afterlife itself through sheer force of musical awesome.
If a singer songwriter extraordinaire, who walked to the depths of Hell and back using only their six string guitar to get themselves through the gates, starts putting out prophecy in song, I think their religion is going to last. The coolness factor alone should ensure that. (Not an exact analogy, but pop culture afterlife is separated into different parts and Hell is the one with depths.)
All of that said, the transmission really, really sucks.