Let me spell it out, BTW in more detail:
Reincarnation: Your soul upon your death goes to find a new body, usually a baby. You sometimes remember your past life. Sometimes everyone does this. Sometimes you are special. Sometimes you remember ALL your past lives, sometimes you just remember one. Whatever the case, usually, everyone does it, you're just the only one to remember, usually because someone, somewhere screwed up.
Maybe you weren't supposed to die and god felt bad. Maybe you were supposed to die, but you were so nice you deserve a few perks and beanies in the next life. Who knows? The Author Knows. Expect it to be set up and never mentioned again in the first chapter, because it doesn't matter. We got a fish out of water story to tell!
Transmigration: Your soul is put into a new body. This CAN include a baby's body, but usually is a body much more mature. The implications are, you are not supposed to be there. The previous occupant was booted and you took over. Sometimes the invader gets "left over memories" from the previous occupant, but the personality and 'free will' of the original is absent. Usually you get nothing from the previous owner, but you have the perk of, "I REMEMBER THIS BOOK" and so the MC can at least GUESS what the previous occupant should know.
Past Life Intruding On Present Time: This is a strange one because it can be either of the previous, in its own way.
A) PLIOPT (Reincarnation): You are Usually you are "reincarnated" You live your life, then you "remember" stuff from your previous life. This usually has some sort of trigger event, like a bump on the head, or whatnot. In this version, usually, the past life is the passive personality and only serves to grant the new "life" information. Like "I read a book in a previous life so I know the plot of this world OMG I'm in an OTOME GAME."
B) PLIOPT (Transmigration): In this version, you are put into a new body and you MERGE with the current occupant to become a gestalt personality. Technically this is a transmigration, but more of an invasion. Usually in this method, the original personality becomes overwhelmed by the invading personality and takes over completely.
C) PLIOPT (Aggressive Reincarnation): Same as the reincarnation above, but the current personality is usually suicidal and wants to die, so they are trying to Nope out of existing, so the previous 'past life' takes over completely. This usually only happens in cases where the current personality wants to die, tried to kill themselves, or succeeded in killing themselves.
Regression: This means that you traveled back in time and remember everything that happened, usually when you die. There are many flavors
Second Chance Regression: Usually someone, a villainess or someone who really screwed up feels REALLY BAD and for some reason they get a second chance. Often not explained in the story, usually GOD or someone goes, 'Yeah, you were a DICK, but I know you are a good guy under it all. What the fuck, he's a second shot at it.' I have no idea WHY god would give a monster a second chance, but hey, we all love a redemption story, so what the fuck. Usually you only get one second chance.
History Erasure Button Regression: Usually the MC dies in a horrible way that was wrong and unjust. Someone else figures it out afterwards and feels horrible. Dad, Emperor, Husband, Crown Prince, some dude, usually. The MC is usual female and was just a saint or sucker, or just misunderstood and her death was tragic. So the History Erasure Button is hit, whatever it is, time ie rewound, but for some reason, only the MC knows that time was rewound. The person hitting the button (or magically maguffin) never seems to remember anything. or maybe they feel really guilty and don't know why.
Ground Hog Day Regression: The MC fucks up and dies. Time is reset. It keeps getting reset until the MC figures out how to get it right. This might be magic, this might be a transmigration, this might even be because he's in a video game and keeps going back to the save point. Usually it goes back YEARS, but months or even days is possible, but usually you get a couple of years to fix things.
Revenge Regression: A rare type. The MC figures out how to regress time out of REVENGE. Very popular among Chinese stories, especially involving Zombie outbreaks. The world goes to shit, but the MC figures out how to advance his chi by taking magic pills and sitting under a waterfall, thus reverting time back to before the zombie outbreak. They stock up on toilet paper, guns, and condoms because they gonna fuck all those bitches who pissed him off. Although if it's Japanese version, expect it to be some guy treated like shit by his adventuring party, and he's gonna make them die in the most graphic of torture porn you can imagine.
Time Power Regression: This version, the power is baked into the story. The MC's power is reset time. Maybe a day, an hour, a week, a save point. Unlike ground hog day regression, the MC is in control of the regression, so he's basically god and cannot lose because, if he loses, boop, reset the day.
ITS A SIMULATION: This is a new one popping up lately. The MC is a simulation of a Normal guy who happens to find himself stuck in an android body, or a Space Ship computer, or whatnot. Basically, any of the above, except that it's not magic, it's SCIENCE(tm) We MEAN IT. No No No. No magic here. Just Microchips and AI making a fake japanese 12 year old kid who was bullied in school just like the target demographic because REASONS. It's all very science-ish. We promise.