A sodium atom has one outer electron, and a carbon atom has four outer electrons. How might this difference be related to the types of compounds formed by atoms of these two elements?

The number of electrons in the valence shell of an element is the principal determinant factor of the kind of chemical bonding it will be involved in. For an element that has only one electron in its outermost shell, such an element will donate the electron to another element which need only one electron. Thus, such an element will undergoes electrovalent bonding. For an element which have four electrons in its outermost shell, such element will prefer to share the electrons will other elements who need such in order to become stable, thus, such element will undergo covalent bonding.