The stem has the functions of water and minerals delivery from the roots to the leaves, and organic materials from the leaves to the roots, and also performs the integration of roots and leaves from the structural point of view.
Young stems have chlorophyll cells and are coated by an epidermis unistratified (a single coat or stratum of cells), as the grass, that can still have over them, a protective cuticle, externally.
Pelas plantas que crescem muito em espessura (transformando-se em arbustos ou árvores), a epiderme é substituída por vários tecidos que formam um revestimento particular e complexo.

O mais externo é denominado periderme (células mortas).
By plants that grow very much thickness (turning into bushes or trees), the epidermis is replaced by various tissues forming a particular and complex coating.
The outermost is named per-dermis (dead cells).
Stems generally are aerial structures that grow vertically. There are stems that grow horizontally, often underground that can be distinguished from roots because they have gems or vegetative buds, from which branches and leaves can develop.

Leaves can be of all possible ways.
A leaf is formed by a petiole, and a flat surface with two faces, the limbo, covered by ribs, and it`s originated from a side gem on the stem.
The leaf serves to photosynthesis, action of the sun on raw sap to change it into elaborate sap, which will be taken to the different components of the plant.

In the link hereunder, of UFU Biology Institute, the different classifications are defined according to the petiole, the shape of the limbo, in function of the leaf apex, enervation or venation, from the vascular bundles of the stem, etc.

Some plants have modified leaves to perform specialized functions, such as the leaves of insectivorous plants, that capture the insects, and the thorns of cacti.

Wikipedia : Botanical explanations