User blog comment:Alemagno12/Huge Ordinal Analysis I: Z 2/@comment-30004975-20180204184704/@comment-1605058-20180204190527

Not quite "yes". Just a formula is an order (actually, not even that, just a relation, but in practice this is never a worry). A well-order is an order (i.e. such a formula) which satisfies certain extra condition (transfinite induction holds).