Oxygen is found in 3 forms: nascent (O), molecular (O2, the most common) and ozone (O3). Nascent oxygen, due to its electronic configuration (i.e how many electrons it has and how they're spread out across its electronic shells) is unstable, and tends to quickly form bonds with another O, forming O2. This is also the case e.g. for hydrogen, which is usually found as H2.
You can find O in this form in some environments, in the upper atmosphere there is enough UV radiation to break up O2 into O.
I don't know if anyone is interested but there would be more versions too. Solid oxygen (red oxygen) at high pressure used to be thought of as O4, tetraoxygen aka oxozone. But if you look at it with x-ray crystallography it's O8, octaoxygen. Cool huh
Those are the 7 that form diatomic molecules not the only elements that form covalent bonds with other atoms of that element. The s block excluding hydrogen, d block and f block are all metals and are held together with metallic bonds which are a type of covalent bond. Mercury forms weak, transient metallic bonds in its elemental form but robust bonds in the Hg2(2+) dication. Sulfur, Selenium and Tellurium form rings and chains, the former being typically 8 atoms and the latter being hundreds or thousands of atoms in length. Phosphorus is in the form of P4 molecules in white phosphorus and is a network covalent solid in many of its other allotropes. Eg. black phosphorus is a series of stacked undulating chicken wire sheets. Arsenic and Antimony similarly adopt this undulating chicken wire sheet structure as well. Bismuth, lead, polonium, aluminum, gallium, thallium and tin are all metals held together with metallic bonds. Carbon, silicon and germanium commonly form the cubic diamond structure although carbon is most stable as graphite (stacked chicken wire) and can form molecules like fullerene and nanotubes as well as chains (carbyne). Boron tends to form crystals containing icosahedrons. The only elements that rarely react with other elements let alone form covalent bonds with one another in bench stable compounds are the noble gases: Helium, Neon, Argon, Krypton, Xenon and Oganesson.
The stuff around us is made out of molecules. Most molecules are made out of more than one atom. Oxygen, the gas, is made out of oxygen molecules. An oxygen molecule is made out of two oxygen atoms. So O2. When you hear "pure oxygen", it's about the substance oxygen (O2), as in pure from other găsesc, not the element oxygen (O).
Now you can also have O or O3 molecules, but those have an electric charge (aka ions), so they're unstable and prone to bond with other elements or to break apart. A gas made out of monoatomic oxygen would be extremely reactive.
Small addition: I wouldn't call O3 (Ozone) charged. It "only" has some partial charge like water (H2O) does, but overall it has the same number of protons and electrons.
Now you could have ozonide (O3-), but that's definitely a way more rare case.
In its natural gaseous state, oxygen is generally found in pairs, hence O2. I guess when you saw "pure oxygen", this meant gaseous oxygen without any other gas normally found in the atmosphere.
So no nitrogen, or carbon dioxide, just oxygen.
In the form of O2 of course!
Very few elements are composed of individual atoms that arent part of a molecule or crystal in their native form under ambient conditions. Individual Oxygen atoms dont have a full shell of electrons. They are extremely reactive for this reason and will pair up to form the considerably more stable O2 molecule. As for why it is more stable, when atomic orbitals interact with one another to form molecular orbitals, the number of molecular orbitals that form is equal to the number of atomic orbitals used to form them. Generally there are two classes of molecular orbitals: bonding and antibonding. Bonding orbitals contribute constructively to the formation of bonds. Antibonding orbitals contribute destructively to the formation of bonds. I.e they weaken bonds. There are a few analogies that can be used to sort of understand what is going on. Constructive interactions are like pushing someone in a swing at just the right time to add to their back and forth motion OR swinging a jump rope at the right time to maintain the wave. Destructive interactions are essentially the opposite of this. An analogy would be pushing someone in a swing at just the right time to slow their motion until they stop or swinging a jump rope at the right time needed to cause its motion to slow until it stops oscillating. If you have experience with tuning forks, youll also notice that if you couple two vibrating tuning forks together you get two separate sets of possible frequencies. One lower and one higher. This has the effect of stabilizing the system. Something similar happens when molecular orbitals form from the interactions of atomic orbitals from individual atoms forming molecules. You can also visualize this extra stability in the molecular orbital diagram for O2 vs the individual atoms: https://chem.libretexts.org/Courses/Pacific_Union_College/Quantum_Chemistry/09%3A_Chemical_Bonding_in_Diatomic_Molecules/9.10%3A_Molecular_Orbital_Theory_Predicts_that_Molecular_Oxygen_is_Paramagnetic
Except for noble gases, single atoms are usually quite unstable and will prefere to release some energy to settle into a more stable molecular configuration.
I asked this question to my nurse in the hospital as a kid (I was a sick child and my grandfather entertained himself and I by teaching math and science...it didn't take). She said that O2 is pure "breathable" oxygen. I'm not sure if that's correct but it was something my eight year old brain could wrap itself around.