((Yep, nenjin, you're in the right zone, SFAICT; you ninja, you...))
The difference is that "the whole Corona" presents a dozen or more (maybe a lot more, depending upon how it crumbles) biomarkers that the immune system can later spot and immediately jump on. And even if the spike in the new variant is radically different, there's going to be a lot of other common features.
The vaccines (not being whole-Corona, either weakened or 'killed' or mushed up) tend to just present (one, maybe more than one, version of) the spike, which doesn't give the same breadth of preparedness (edit: though it is probably the single best target to actually try to target, which is why we do).
Right now, Corona is being selected 'in the wild' for variations that do better, which with a spike-based vaccine in its trial-population (the 'terrain' across which it wishes to survive) means spike-mutations are more likely, as if to sneak by the cops with a photofit by wearing a different style of spectacles (depends on the cop, though works more than without).
It at least takes some of the selective pressures off other changes (the efficacy of the internal payload, for example) and booster shots newly trained to represent "Groucho glasses"-wearing spikes (as it were) can be brought in for those that are sufficiently escaping the previous narrow net and developed other more insidious[1] mutations by chance/mix'n'match.
I'm not happy with actively helping the virus find more solutions to get past the immune system (vaccination + live-inocculation, times a huge population = higher chance of breakthroughs that surprise everyone a little further down the line), but that's just notoriously unreliable statistical instinct and someone else (whose Chair of Immunology is more than the "arm-" variety) should probably run through the numbers and mechanisms involved, rather than liddle-old-me.
[1] Could be more subtle, for longer infectivity upon others, rather than actual greater illness and ultimately deadliness on a per-case basis. In fact, it's likely that'll be the long-term drift, the longer it goes without extinguishing itself by killing off its 'hosts'.