These are particularly 'low-level' bonds (a technical term meaning that a bond impacts the participants' minds significantly and at a fundamental level). Unlike other types of mindbond, they cannot be broken except by default (see below).
Demons usually say "binding" and "bound (to)" as opposed to "bonding" and "bonded (to)". They don't use the terms "bondee", "kebound" or "bondmate" to refer to participants in a bond.
The demon/hellhound binding mechanics, as designed into hellhounds (which are a created species; see their section), were based on demon/demon binding but altered for heavy skew (see below) to the demon's side and to introduce a desperate drive that virtually forces a single hound to bind.
Deepcore communication is entirely secure with no leaking or possibility of being overheard. Breaking the secure link is equivalent to destroying the bond, and may be considered impossible under normal conditions.
It is broken by the death of one participant, which in almost all cases results in the death of the partner. (If it's a demon/hellhound bond, the hound will definitely die. A demon has a small chance of staying alive.) The alternative to death is very unpleasant near-total destruction of the survivor's mind.
The mental state of one participant can 'bleed' (a technical term meaning, roughly, 'leak') from one participant to the other. This can be used deliberately by a partner with strong enough willpower to affect the partner's mood.
Communication happens as fast as the slower partner can think, and is not impaired over long distances.
Skewing is (you guessed it) a technical term. It concerns the balance of power between mindbound partners.
A demon/demon bond is unskewed, with neither partner having exclusive control over the other.
A demon/hellhound bond is heavily skewed to the demon, with the demon able to take full control over the hound. Technically the demon can make the hound do anything, including forcing extraordinary feats of agility or stamina -- but the adverse aftereffects can leak over to the demon, making this uncomfortable.
Hellhounds have low stability, and forming a bond with one will lower a demon's stability (unless its was lower to begin with). The companionship, however, means they become less bored, and if a pair can avoid getting into fights, the adjusted life expectancy is actually longer than a single demon.