Long ago when I originally played Chrono Trigger, I tried to repiece together the storyline, and where and what Crono's effect on time really changed things. So I though I'd write it down today.
Here's how I can understand and/or speculate on CT events.
65,000,000 BC : Lavos crashes into Earth, which eradicates the Reptites, that should have won over Humans.
12,000 BC : Zeal kingdom thrives on Magic and technology, and tries to draw more out of Lavos, but fail at it. The result sends Janus and the 3 sages into other timelines. Trying to draw too much power from Lavos made it wake up and destroy Zeal, including all of the royal family, which led to the end of magic.
It's also shown that the destruction of the Mammon Machine with the Ruby Knife turned it into Masamune, but how it happened in the original timeline is not explained, presumably Schala or Melchior could have done it. It's also unclear how the Masamune went down through the ages, or how it received the two souls of Masa and Mune that were in Zeal before that.
600 AD : Queen Leene was rescued possibly by Frog and the castle guards. While Masamune was not restored in that timeline, Frog possibly led a secluded life. Magus tried to summon Lavos, but was quite possibly killed by it instead. Due to a simple disapearance rather than a defeat, Magus is still venerated in Medina village later on, and the feud between Humans and Fiends is never truly resolved.
1000 AD : Nothing happens just yet, it's the start of the entire story.
1999 AD : Day of Lavos
Now if you start at the point that Crono starts messing with the timelines.
600 : Queen Leene's rescue was changed due to the mistaken identity with Marle. It led to the whole undoing of Yakra, his false chancellor ploy, and was the reason that the prison was built in 1000 AD, which also led to the second false Chancellor in 1000 AD later.
Going to the future didn't affect anything. Going to 65,000,000 BC served one thing, it did serve to explain a link between the Dreamstone that Ayla possessed and the Zeal kingdom, possibly out of the same lineage of tribe leaders. This would make Ayla and Schala blood related though there's millions of years between then.
Restoring Masamune brought down Magus, which is the major turning point in the entire CT story. Instead of being killed, he was sent back to 12,000BC, where he acted as counselor, an oracle, since he already knew about events. His guidance finished up the Mammon Machine and the Black Omen, which were not supposed to be finished in the original timeline.
Magus' effect increase the energy draining potential and stablized it, so while it still destroyed Zeal, it left the Queen alive. Although we don't see it in the story, we can suppose that Janus and the 3 mages were also sent back during those events, although they differed from the original timeline.
Most of the other happenings are minor changes, like changing the greedy mayor to a generous one, or helping Lucca's mom and the forest. Medina village actually gets a little more mellow after they stop venerating Magus, but they are outright friendly when Ozzie is taken out as well in the optional sidequest.
If you tack on Chrono Cross's storyline to it it gets even more complicated.
Humans are called 'Lavos Spawn'. Lavos eradicating the Reptites had the effect that Humans became dominant. Without Lavos, Reptites would have dominated the planet most probably. Thus Lavos helped humanity.
Chrono Cross starts from that fact, playing off on alternate dimensions starting from specific events in time. Lavos is one of those pivotal moments, where Humans win over Reptiles and dragons. That's why you see Dinopolis opposed to Chronopolis, the two most advanced cities made respectively by Reptiles and Humans.
Schala being a major part of the story, I'm still unsure what part she played in the 'fusion' with Lavos into the Time Devourer, but one thing is sure, Serge ends up stopping both Dragons trying to eliminate humans, and Lavos trying to eliminate pretty much everything else. No pressure at all, right Serge?
Another more hazy part is the Masamune, we can't be sure how it reached all the way in that island group between 600 and 1020 AD, and how it got that evil blade reputation and power, although it may just be a prank from the souls of Masa and Mune for all we know, being bored out of their mind after Frog had no more use of the sword.
A reference to Robo is also made, as the giant computer that the dragons try to get rid of called himself Prometheus, allegedly built by Lucca. Prometheus was Robo's true name, which Lucca quite possibly reused as a memory. In CT's final anime cutscene, Lucca is even walking around with a mini-Robo she probably built.
It's all little ties that show that CC and CT are related. That you want to consider them true sequels or not is your choice, but the entire idea of time travels and alternate dimensions already says that the things we know from CT probably don't fully apply anymore. You could consider that CC is an alternate dimension of CT, where Lavos wasn't destroyed and lived on thanks to Schala's power.
Making CC go into time travel would have otentially messed up the already established story and timeline of CT, so the alternate dimension thing was a good idea in that aspect. It was a good way of keeping the 'time travel' to some degree.
