For example like HCl, why isn't it a hydrogen bond?
Hydrogen bonding is defined as an electrostatic attraction between a hydrogen atom bearing a partial positive charge in a molecule and an electronegative element of another molecule. The partial positive charge is the result of a dipole, caused by an electronegative element, such as F, O, or N. The other electronegative element to which the partially positive hydrogen is attracted to is also usually F, O, or N.
Here's the IUPAC definition; note that it does not exclude the possibility of hydrogen bonding in molecules such as HCl:
A form of association between an electronegative atom and a hydrogen atom attached to a second, relatively electronegative atom. It is best considered as an electrostatic interaction, heightened by the small size of hydrogen, which permits proximity of the interacting dipoles or charges. Both electronegative atoms are usually (but not necessarily) from the first row of the Periodic Table, i.e. N, O or F. Hydrogen bonds may be inter-molecular or intramolecular.