When the pull is uneven
Now take two atoms whose electronegativities are not the same.
In hydrogen fluoride the two atoms share a pair, but fluorine is considerably more electronegative than hydrogen. The shared pair is therefore pulled closer to the fluorine atom than to the hydrogen atom, and the electron distribution is no longer symmetric.
The fluorine end acquires a very small negative charge and the hydrogen end a very small positive one. These partial charges are written δ− and δ+, and the effect is called polarization.
A partial charge is not an ion
δ+ and δ− are far smaller than the full +1 and −1 of an ion. No electron has been transferred; one has merely been pulled off centre. Taken as a whole, HF is still a neutral molecule.
Two kinds of covalent bond
The two atoms differ in electronegativity, so the bonding electrons are distributed asymmetrically and partial charges appear. HF and HCl are examples.
The two atoms have equal, or very nearly equal, electronegativity, so the bonding electrons are distributed symmetrically. H2, O2 and N2 are examples.
What decides polarity
Not how strong the bond is, and not how many pairs are shared, but the difference in electronegativity between the two atoms. No difference means no polarity, whatever else the bond is doing.