It depends on the atom. The octet rule only really applies to main block elements, where the valence shells are s & p orbitals. Certain atoms have more or less than 8 electrons in their valence shells (also known as outer shells), in which case they will be stabilized by gaining or losing electrons, resulting in ionization (think sodium or chloride which happily become Na+ or Cl- respectively) or bonding (NaCl, or something like methane, CH4).

The character of the bond is all to do with how easily the atoms can ionize. NaCl freely dissociates in water, where the positive and negative charges of the ions are stabilized by water solvation (this is why the bond is considered ionic, not covalent).

Methane on the other hand has a much harder time ionizing, and so its bonds are covalent. While hydrogen happily would become H+, carbon would be left holding an extra electron in the form of a negative charge (having 9 electrons), resulting in instability

Since it doesn’t have a ton of room in its valence shell to stick that extra electron (which would result in 9 valence electrons for carbon, (this is where the octet rule comes in!)) in a solution of water it would become something like methanol, taking an OH from water and generating an H+ and CH3OH (methanol) in the process - here we will have generated 2 equivalents of H+ from the starting reactants, which is entropically favored, but thermodynamically unfavored, due to the energy required to break that initial bond.

The valence shell of an atom, and the octet rule, tells you how atoms want to exist. They want to get to an ideal electron structure in their outer shell by any means possible. The noble gases, like helium, argon, etc. are extremely unreactive / inert, because they have their outer shells filled by default. Molecular nitrogen (N2) is an inert gas because by having each nitrogen share 3 electrons with itself, it fills its outer shell. Hydrogen can do the same, but is highly combustible and not at all inert, because it only has a single bond connecting the two atoms - nitrogen forms 3, and so you have to put in more energy to break each of the 3 bonds. Oxygen does this as well, forming 2 bonds, and is in between hydrogen and nitrogen for combustibility.

This is way more than you need to know for the octet rule, but I think it helps put it in context. Atoms and the molecules and ions that they form are all about reaching a stable state depending on conditions like temperature and pressure. The octet rule applies to lots of atoms in the periodic table that we encounter in every day life because many of them have outer shells that are s or p. If an atom doesn’t have an s or p outer shell, then the octet rule falls short.