What is the relationship between diatomic molecules and diatomic elements?

Hint: Diatomic elements are the molecules which consist of two same elements covalently bonded to each other whereas the diatomic molecule may or may not have two same elements bonded to each other.

Complete answer:
Diatomic molecules are the chemical compounds which are composed of only two atoms of the same or different chemical elements. If a diatomic molecule consists of two same elements like ${H_2}$, then it is said to be homonuclear otherwise, if a diatomic molecule is composed of two different chemical elements like $HCl$, then the molecule is said to be heteronuclear.
Now, we know that a diatomic element is a molecule which consists of two same elements that are covalently bonded to each other. So, basically it refers to a homonuclear molecule. There are only seven diatomic elements in which five of them are hydrogen, nitrogen, fluorine, oxygen and chlorine gases, at normal pressure and room temperature and are generally known as elemental gases. Bromine is liquid and iodine can be a liquid or a solid depending upon the condition in which it is considered.
Thus, we can conclude that every diatomic element is a diatomic molecule but every diatomic molecule is not necessarily a diatomic element. Hence, the relationship between diatomic element and diatomic molecule can be expressed as: diatomic elements are the subset of diatomic molecules.

Note:
It is important to note that subset here refers to a part of a larger group of related things. Also remember that diatomic elements are always non-polar molecules because the electronegativity difference between the two same elements will always be zero.