  Irreducible Artin groups of finite type can be parametrized via their
associated Coxeter diagrams into six sporadic examples and four infinite
families, each of which is further parametrized by the natural numbers. Within
each of these four infinite families, we investigate the relationship between
elementary equivalence and isomorphism. For three out of the four families, we
show that two groups in the same family are equivalent if and only if they are
isomorphic; a positive, but weaker, result is also attained for the fourth
family. In particular, we show that two braid groups are elementarily
equivalent if and only if they are isomorphic.
  As a consequence of our work, we prove that there are infinitely many
elementary equivalence classes of irreducible Artin groups of finite type. We
also show that mapping class groups of closed surfaces - a geometric analogue
of braid groups - are elementarily equivalent if and only if they are
isomorphic.
