The norm, "under the tree" and "in the shade". Poetically, "in the shade of the tree" means, the shade encompasses him.
EX: I stood in his shadow.
EX: I stood in the shadow (that) his body gave forth.
EX: I stood in the shadow of his body. awkward; it means the shadow is inside his body.
EX: I sat in the shade of the tree. (ambiguous; either, "the shaded area of the tree" or "the shade inside the tree")