  We construct a coupling between two seemingly very different constructions of
the standard additive coalescent, which describes the evolution of masses
merging pairwise at rates proportional to their sums. The first construction,
due to Aldous \& Pitman, involves the components obtained by logging the
Brownian Continuum Random Tree (CRT) by a Poissonian rain on its skeleton as
time increases. The second one, due to Bertoin, involves the excursions above
its running infimum of a linear-drifted standard Brownian excursion as its
drift decreases. Our main tool is the use of an exploration algorithm of the
so-called cut-tree of the Brownian CRT, which is a tree that encodes the
genealogy of the fragmentation of the CRT.
