Let's clear up some misconceptions. Atoms are the very simplest units of matter that are uniquely different for each element. The elements on the periodic table match up one-to-one for each type of atom there is in the universe as we know it. Think of atoms as our fundamental building block for all matter. Standard chemistry and chemical reactions do NOT break atoms into smaller pieces. The atom is very very robust and stays that atom forever unless some extraordinary event of high energy occurs. Those events like that fit into a category called nuclear chemistry and we will touch on it eventually. For now though, we shall leave the atom intact.
The name of the atom is the element name. An iron atom is different from a carbon atom. And, although atoms are built from the same subatomic particles (protons, neutrons, and electrons), the elements are uniquely different in their properties in that each atom is built with a different number of protons, neutrons, and electrons. The number of protons is the key to which element the atom is. 6 protons in the nucleus is a carbon atom. 26 protons is an iron atom. Gold is an atom with 79 protons in the nucleus. All neutral atoms (no charge) have the exact same number of electrons as they have protons. Neutrons vary but will typically be the same as the number of protons (smaller atoms) or 1.5 times the number of protons (larger atoms).
Molecules need a combination of atoms to be complete. The minimum is two atoms. Two atoms that are bound together via a chemical bond make a molecule. In this case, a diatomic molecule (prefix di- means two). The air you are breathing has two major diatomic molecules, nitrogen gas and oxygen gas. The formulas for them are N2 and O2. Those are very small molecules relatively speaking. Molecules can get much much bigger. Some molecules in your body are incredibly large consisting of thousands of bound atoms with molar masses in the hundred thousand range. A molecule is the simplest repeat unit of most of matter. Note the difference in the figure below:
The circles actually represent a three dimensional sphere. The range of atom sizes actually shows the entire relative range of atom sizes from the smallest (hydrogen) to the largest (cesium). The molecules are all combinations of atoms in some way. There are two simple diatomic molecules (2 atoms) while the others shown have three and four atoms.
Also, don't get confused with atom/molecule and element/compound either. Stick with the definitions. A compound is any substance made up of more than one type of atom (element) - which means there are only two compounds shown in the figure above - the two on the far right end which each have 3 atoms in them. So sodium chloride (NaCl) is a compound. Water, H2O, is a compound - and a molecule. Also note that two of the molecules (the two diatomic ones) are elements (not compounds) because the molecule is made out of only one kind of atom which means it's an element. So are all compounds molecules? and all elements are atoms? No, I just pointed out that some elements can be made up of molecules.
As pointed out on the figure, certain elements exist as molecules and not atoms. Like the two examples of nitrogen and oxygen I mentioned earlier. Those are both diatomic molecules AND they are elements - plus they match up well with the little purple diatomic molecule shown. There are other molecular elements as well. However, most of the elements are depicted in reactions as just the single symbol for that element. Most all the metals are this way. So iron in a reaction scheme is just Fe(s) if it is in the solid state. So know that there are special cases of elements as molecules.
There is one more specific thing I'd like to point out. When true positive ions and negative ions get together, they create an entire lattice of alternating positive and negative charges (cations and anions to be specific). Even though the entire cluster/lattice is all interconnected with ionic bonds, we only show the basic repeat unit in formulas. That is why sodium chloride is just NaCl. NaCl is the repeat unit. We call these repeat units in ionic compounds formula units. Technically, these are NOT molecules. A true molecule has a beginning and an end - held together with covalent bonds. Water is a great example of just 3 atoms (H, O, and H) held together with 2 bonds (two identical H‑O bonds).