Explaining Applicative functor in categorical terms - monoidal functors

I'd like to understand Applicative in terms of category theory. The documentation for Applicative says that it's a strong lax monoidal functor. First, Wikipedia page about monoidal functors says that a monoidal functor is either lax or strong. So it seems to me that either one of the sources is wrong, or they use the terms differently. Can anybody explain that? Second, what are the monoidal catego