...sorta but not really. It's just two different time periods and/or timelines. so...eh maybe you are right. the comic book way, hah.
the storylines are essentially still true between all of them, it's just that the new series is basically a prequel for the former series, with a handful of the characters replaced by new actors. I also don't see any suggestion that the way they are doing the new Jean Grey and Cyclops will essentially be different than the storylines from the earlier movies--it could still essentially be the exact same plots, as no origin story was actually replaced, like was done 3 times with Spider-man or the FF or whatever. ...I think the only x-related storyline that has gotten an actual do-over is Deadpool, and it seems that the first Wolverine movie is basically ignored as having ever existed in the rest of the X-Men/Wolverine stories...though I guess this all depends on how the do the Phoenix thing with this one. The original series, Prof X had long ago discovered and knew about the Phoenix, but I think that Jean Grey was much younger? I guess it wouldn't work here because I don't think any of the other X-Men knew about it in the earlier series, before it manifested. I guess they would know here....oh and of course now I recall that they showed that brief bit with Xavier and Mags meeting young Jean, and I don't think it was anything like the stuff in the current series....so I'm probably completely wrong.
the connection between the two eras is Hugh Jackman's Wolverine (though I think he is officially done?), and his storyline remains cohesive across all of the series, kinda tying them together in the different plot times that they take place.