For A to dominate B, A has to be at least as good (i.e. no worse) than B in every objective under consideration and A has to be strictly better than B in at least one objective.
Every solution in the Pareto front set dominates every solution not in that set: is at least as good in all optimization parameters and strictly better in at least one.
Among the front set, there is no mutual dominance: if we pick any pair out of the set, one may be better than the other in one or more parameters, but worse in one or more. If it were not worse in one or more than the other, that other would not belong in the front set due to being dominated.
Consider a space where we have two solutions. One is no worse than the other in every objective, and strictly better in one objective. Here, our Pareto front set contains that one solution and the other one is not in the set. Yet, the one not in the set is not beaten in every objective, just in that objective where the dominator is strictly better.