One has the definition of a monoidal equivalence as in definition 12 of Baez's Some Definitions Everyone Should Know.
I have also seen monoidal equivalence defined as a monoidal functor between monoidal categories which defines an equivalence (i.e. a fully faithful, essentially surjective functor) in the sense of definition 5 in Baez (link above).
I wanted to double-check that these two definitions are distinct. If anybody has any intuitive insight as to why/when the two are employed, that would also be appreciated. Thanks.