Buddhism nearly neglects the body, seeing it as one root of illusion. So buddhist spirituality tries to leave the body behind and there are certain ways to vanquish or bear down the body.
In Taoism bodywork is the very first step towards spirituality. Building, developing the body is not only a prerequirement, it is even part of spirituality.
While there is a basis for these shorthand characterizations, one of the factors that makes (at least some strains of) Japanese Buddhism unique is the fusion of Taoist and Buddhist influences that developed in T'ang-era China and was transmitted to Japan. This can be seen quite clear in the Shingon doctrine of "Sokushin Jobutsu" or "the attainment of Budhha-hood in this very body."
In this formulation, the body is regarded simultaneously the root of illusion AND the root of enlightenment. This is relevant to the larger discussion precisely because the Shingon and Tendai traditions were the ground out of which most extant sects of Japanese Buddhism arose. Doctrines vary from sect to sect, but it is quite possible that a Japanese instructor might proceed from a basis that is a blend of Taoist and Buddhist traditions.
Plus, also, what NagaBaba said....