There are a few terms that have entered the popular culture Lexicon that are nothing but gibberish, and "soft reboot" is one of those terms. It means absolutely nothing because it describes a creative process that doesn't exist. You either reboot something completely - whereby you completely discard its existing continuity - or you retain the continuity of what already existed and add new installments to said continuity.
Period.
Making the claim that a fictional property has undergone a "soft reboot" is an immediate signal that you don't actually have a clue as to what you're talking about.
If you say so mate. Doesn't change the fact that Fox retroactively stitched together the FC chain of events, with the Post-X3 chain of events in DOFP.
Things like Logan getting the adamantium 15 years prior to X1. Even though XM Origins had him get the metal in 1979 (during the 3 Mile Island event). X1 being set in 2005.
Charles stating in X1 that he was 17 when he met Erik, but in First Class they met in 1962. 18 years after (a presumably 10 year old) Erik and his family were sent to Auschwitz in 1944.
The origin of Magneto's helmet. Charles is surprised to see he couldn't read Magneto's mind in X1, but if FC had happened, then Charles would've known about it prior.
Xavier walking in 1984 (X3) but being crippled in 1962 (FC) Magneto.
Mystique growing up with Charles in FC but in X1-X3 she never speaks nor acknowledges any history with him. Because there was none.
The two Deadpools (played by the same actor decades apart), the two Sabertooths, the two Toads, the two Bolivar Trasks (X3 and DOFP), the two Emma Frosts, the soon to be two Gambits etc.
There are more instances. The point is, there was no master plan to have all of this fit together when Fox started in 2000. Fox doesn't care about continuity gaffes, unaswered question (like how did Xavier come back to life after X3) and just keeps moving forward with whatever the agenda is at the time. Plans change, the narrative changes. In 2011, FC was both a prequel (originally Magneto Origins, like Wolverine's) and a reboot to the X franchise. In 2014 however, both iterations were married together. Like this was their plan from the start. It wasn't.
Terms like "hard" and "soft" used to describe reboots are meant to demonstrate the level of disconnect from a previously establish movie or series of movies. TASM movies were hard reboots, because they started from scratch with an origin and all new cast. Originally, before the Marvel deal, Sony was talking a soft reboot for Spider-Man because they didn't want to start over again completely with Spider-Man again. Which worked out for Spidey in Civil War. He's already been bitten, has web shooters, Uncle Ben is dead, and he's helping people.
Contrast to Prometheus (Alien) which was said by Scott to be both a prequel and soft reboot of his Alien franchise. All the trappings the audience recognize are there, but it's only tangentially connected to the original Alien and Aliens.
