I've always thought of them as just periods of time, and a long the way, whether we're going forward or back in time, we are making changes that alter our own reality.
That is the whole basis to this game, to me anyway, is to alter timelines. In CotD for example, Richtofen went too far into the future by mistake, and in doing so changed our modern world, the 2000s, into a zombie infested hellhole. I'm sure he was planning on going to a time where everything wasn't frozen, making it easier to get the golden rod. But instead, Richtofen got lucky and was basically handed the Golden Rod, he then went back in time to use the Golden Rod with the Focusing stone to create the key to the pyramid.
Fast forward to Moon, the golden rod is in Richtofen's possession, well into the current time of our own, thus making CoTD disappear from the timeline, not that Romero and cast didn't go to the area and film a movie, but rather it was a successful attempt that wasn't ruined by Richtofen, because he already has the rod and doesn't need to go to that area in our current time. Also not saying CoTD and Moon were on the same day, just in the time period of the player, us.
If say, Takeo had managed to go back in time, and hide the golden rod in another location, he could have prevented Richtofen's past self from finding it, at least so easily.
It's kind of the same for Origins, Samantha is rewriting the game more or less, so she doesn't lose power, or maybe so her and her father can just have a normal life. This is where it all blurs for me, the true intention of Samantha, all we know for sure is she doesn't want Richtofen to have his power. How she is aware of her fate before it actually happening I don't know, but to me she is aware eventually Richtofen will steal her power and lead to the worlds end. Freeing her merely allows her to create a fresh start, but perhaps some things can't be rewritten, as we hear sirens going off probably signaling an outbreak.
I hope that wasn't too confusing.