Heir of the Ancient Fang enters the battlefield with a +1/+1 counter on it if you control a modified creature. (Equipment, Auras you control, and counters are modifications.)
A creature that is equipped is considered modified no matter who controls the Equipment that's attached to it.
A creature with a counter on it is considered modified no matter what kind of counter it is or which player put it on that creature.
An Aura controlled by an opponent does not cause a creature you control to be modified.
Only creatures can be modified. If a modified creature stops being a creature, it is no longer considered modified.