OK, the discussion of covalent bonding was good. But an understanding of covalent bonding, while necessary for answering the question is not sufficient for answering the question.
Singlet oxygen (O1), molecular oxygen (O2), and ozone (O3) are all breathed in and out by all of us every day. They all exist in the atmosphere, and they all can cross membranes from alveoli into capillaries in the lungs. The difference is what happens after that.
Singlet oxygen is one of the most reactive forms of matter (singlet fluorine is the most reactive, at least in my 1970s era Chem classes). It it formed when sufficient energy is added to a molecule of O2 to break the covalent bonds. High in the atmosphere (the ozone layer), this energy comes from the sun. Closer to earth, this happens whan an O2 molecules collides with another molecule with enough energy transfer to break the bonds. In air, as soon as an atom of singlet oxygen collides with anything, though, it tries to covalently bond with that other molecule to fill its outer shell. The molecule it most often does this with is O2, and that is how ozone is formed.
If you’ll go back to Hawk’s explanation of covalent bonds, and try to arrange the 18 electrons among the 3 nuclei so that each nucleus keeps 8 electrons in its shells, you’ll get frustrated - it doesn’t work out neatly like it did for O2 - electrons move around in a constant effort to find a stable arrangement, but there is not one as stable as for O2. So ozone is a more reactive, less stable for of oxygen than O2, but it is more stable, and less reactive than singlet oxygen.
Inside the body, it turns out that singlet oxygen and ozone can’t substitute for O2. They are physically different - remember that atoms take up a 3 dimensional volume, and don’t fit into the same “pockets” that O2 does in enzymes and and other large molecules that use oxygen. Additionally they are chemically different - they behave in an entirely different manner.
They (ozone and singlet oxygen) are termed “reactive oxygen species” and can lead to to formation of other unstable things like free radicals - for example, an oxygen covalently bonded to a hydrogen with a total of 7 electrons in the outer shells, instead of the 8 that lead to stability. These free radicals quickly react with other molecules, and more or less permanently alter the structure of DNA, proteins, and other crucial molecules. Since alterations in structure lead to alterations in function, this is bad. The body has a repair mechanism to repair this so-called oxidative damage (with the help of Vitamin, C, vitamin E, flavinoids and other antioxidants) but if too much damage happens too fast, the repair mechanisms can’t keep up and cell death, or other irreparable harm is done to the body.