Hydrogen bonding
As the name suggests, hydrogen bonding occurs between molecules containing hydrogen. But it is not enough to have hydrogen alone; firstly, hydrogen must be bonded covalently to either fluorine, nitrogen, or oxygen, producing a strong molecular dipole. Secondly, this dipole needs to come near another fluorine, nitrogen, or oxygen atom, which the hydrogen will then attract strongly.
Why fluorine, nitrogen, and oxygen?
Fluorine, nitrogen, and oxygen are located in the top right of the periodic table, indicating that they are small and have a high electronegativity. When these elements bond covalently with a hydrogen atom (which is a lot less electronegative), the electron cloud will shift away from the hydrogen. This shift generates a strong, permanent dipole, where the hydrogen is very positive. When this hydrogen comes near other very electronegative elements, an attractive force arises between them, called hydrogen bonding.
Why not chlorine?
Chlorine has a similar electronegativity to nitrogen, so why does it not partake in the creation of hydrogen bonding? The reason is its relatively large atomic radius, which means that the electron density spreads out over a larger area. This dilution of electrons will prevent chlorine from forming proper hydrogen bonds. As a result, we categorize the attraction between HCl molecules as regular permanent dipole-dipole forces.
Since hydrogen bonding is a force of attraction between permanent dipoles, it is a subcategory of permanent dipole-dipole forces. Hydrogen bonding is still the strongest intermolecular force and is responsible for the unique properties of water and DNA, among other compounds.