An element is a description of a type of atom, so a single atom is representative of an element but not an element itself. "An atom" refers to a physical entity; "an element" refers to a type of atom.
Atoms are defined by the number of protons they contain in their nuclei. The element of hydrogen refers to atoms that contain a single proton, while helium atoms contain two. An isotope is defined by how many neutrons are in the nucleus, and molecules are described by what atoms they contain. Water, for example, contains one oxygen atom and two hydrogen atoms, so its scientific name is dihydrogen monoxide.