This video here is the first time I've ever heard the term "soft Cboot" (or "ceeboot" or "seeboot" or "seaboot" or whatever the fuck it actually is, because Google apparently never heard of it before either), but I would agree with the definition of it as they put it forward here.
The nuTrek movies are indeed an example of... that thing mentioned in the previous paragraph, because while for all practical purposes, it's definitely a hard reboot of Star Trek, at least as far as the movies themselves go, they finessed it so that Star Trek "Prime" still exists, even for the new universe/timeline (i.e. the presence of Old/Nimoy Spock, for one thing). Which is good, because all the TV shows still take place in Trek "Prime," not the Kelvin timeline thing. And there may come crossovers between the two in the future, or maybe they're already happening, for all I know. (I haven't seen season three-and-beyond of either Discovery or Lower Decks yet [and I pretty much stopped reading that link there after the first couple paragraphs for that very reason], and I certainly haven't read any of the comic books about any crossovers between Prime and Kelvin.)
In any case, it's all just modern video game industry (and modern movie industry and modern comic book industry[1]) dumbfuckery. Nigh useless marketing buzzwords, for the most part, at least given how actual marketing people are uselessly using them, anyway. The words themselves do have specifically accepted meanings, though.
[1] - Or, maybe, not-so-modern in the case of comic books since, as was pointed out in one of the comments under the above video, Crisis on Infinite Earths from way back in 1985 was probably the first "soft c/cee/see/sea/whatever boot."