While media casually refers to any property returning after a long hiatus to be a "reboot," there are actually multiple categories of IP relaunches:
A reboot is where the continuity starts over again with no acknowledgement of previous productions, and the term is drawn from turning off a computer system and turning it back on. Reboots include THE BABY-SITTERS CLUB (2020), BEAUTY AND THE BEAST (2012) and THE PRISONER (2009).
THE BABY-SITTERS CLUB would not have benefited from actresses in their 40s reprising roles they played 20 - 25 years previous to have their characters resume jobs they held as adolescents. BEAUTY AND THE BEAST was unlikely to secure Ron Pearlman and Linda Hamilton to reprise their roles in a TV sequel, so recasting and starting over made sense, as did rebuilding the entire concept of the show (a highly civilized lady police officer and a savage warrior fighting crime) in the context of 2012 society. Rebooting both made sense and I would call these two examples of successful reboots.
However, THE PRISONER reboot is my example of a failed reboot where the PRISONER reboot eliminated nearly every point of distinction about the original 1960s show. The original show was defined by characters known by number instead of name, a strong espionage-conspiracy thirller concept, a daring action-adventure formula and a acidically satirical vein of social commentary. The reboot had characters known by name, no spy elements, little action, no adventure and no social satire at all; it wasn't THE PRISONER except in name.
I would say that reboots are successful when the concept and character templates (if not the characters themselves) can be reintepreted and rebuilt to be relevant to the present day and market. Batman has been relentlessly rebooted and can be made darker or lighter as needed for each era. However, reboots fail when the concept is out of step with the needs of the audience or if the production is incompetent or if the reboot is so disconnected from the original that it may as well not use the same name.
A revival is where the production is set in the original continuity as a sequel to the original production. THE X-FILES, GILMORE GIRLS, SAVED BY THE BELL, PUNKY BREWSTER, GIRL MEETS WORLD and SCREAM all benefitted from being revived when the stars of these properties were working actors and the right age to play older versions of their original characters. They also benefitted from their original storylnes being extremely opportune for sequels.
However, THE X-FILES was a creative failure because despite being a revival, it contradicted or ignored its original (and unfinished) storylines and failed to bring Mulder and Scully to the next stage in their personal and professional relationships the way the other revivals listed above did for their cast. THE X-FILES didn't accomplish the goals of a revival, instead skipping back and forth between ignoring continuity and tying into it, and the results were confusingly impenetrable.
I would say that revivals are successful when the original storylines and characters benefit from resumed exploration, but they fail if the original storylines are too dense, contradictory or confusing for a casual audience who may not have seen or remember the original. They also fall apart if the revival doesn't feel like a new chapter of the original.
THE X-FILES was a peculiar case where the original storylines were too dense, contradictory and confusing for the *writer* attempting to produce a sequel that didn't require the audience to remember much; the writer ended up confusing both the long-time fan and the unfamiliar viewer. And THE X-FILES also put Mulder and Scully exactly where they had been back in the 90s; despite the age of the actors, they felt like they hadn't made any progress.
A rebootquel is where the continuity starts over but acknowledges the previous productions through time travel. Examples include the STAR TREK 2009 movie and TERMINATOR GENYSIS.
I'd say STAR TREK's rebootquel series was a mixed bag. The first movie was strong, enabling long-time fans to accept an altered continuity while being accessible to new fans. The second movie, however, got hopelessly entangled in continuity and callbacks that were obnoxious and clumsy for long-time fans and nonsensical to new fans. The third one was a strong action story that unfortunately couldn't overcome the audience's dismay with the second movie and make enough money in ticket sales.
And TERMINATOR GENYSIS was truly puzzling and counterintuitive; it rewound back to the 1984 time period of the original movie, but then cast off the 1984 setting as quickly as it could, rendering the rebootquel approach pointless.
This tells me that for a rebootquel to be effective, it needs to embrace the specific time period to which the franchise is rewinding but also embrace that it is a new story, not a remake or sequel to an old story.
A deboot is where the continuity rewinds itself to a previous installment and ignores some previous sequels but not the original and possibly a select number of sequels. Examples include TERMINATOR: DARK FATE, HALLOWEEN (2018) and others.
HALLOWEEN's new movies ignore all but the first film; TERMINATOR: DARK FATE ignores all but the first two. HALLOWEEN's sequels were a strong distillation of the original concept and an effective update for a new era. TERMINATOR: DARK FATE was... I liked it well enough, but ticket sales were poor and it's possible that after two bad sequels, an unfinished TV show and long periods where the TERMINATOR franchise had been absent, the audience had atrophied.
In this case, a deboot is an exercise in reverting to the original storytelling template after numerous deviations. HALLOWEEN succeeded because the back to basics, non-supernatural horror of the first film had been lost with the sequels becoming increasingly magical; the deboot felt like a return to form. In contrast, the original TERMINATOR and each sequel had generally featured humans on the run from robots and TERMINATOR: DARK FATE, despite being a deboot, was more of the same and the audience had tired of it and stopped going.
Reboots: Effective when the concept is timeless but the original storylines don't necessarily need sequels.
Revivals: Effective when the characters and storylines of a past TV show benefit from new exploration and can be made relevant in the present day.
Rebootquels: Effective when the franchise has a large audience but also impenetrably dense continuity in need of a new entry point for casual viewers.
Deboots: Effective when the concept has been distorted and a return to the original idea is welcome.