Antaryami Perumal is an in-dweller in all; that is, within sentient and insentient beings Bhagavan is present in a divine form. When one intends to perform Yogam, one can meditate on this form of the antaryami Perumal. Generally, Perumal is present within everyone.
Avesha avatara is when Perumal specifically makes His power (Shakti) or trait/character/form (Svarupa) enter into another being. Antaryami is common while avesha is when Perumal enters his power within specific individuals and through whom he carries out specific acts for specific objectives – an example is Parashurama avataram. Though Perumal is antaryami in everyone, only because Perumal entered into Parashurama (Avesha avataram), he was able to carry out incomparable acts. Similarly, the incarnation of Vyasa. There are many Jnani-s; but only Vyasa complied and categorized the Vedas, composed Mahabharata, Vedanta Sutra, collated the Purana-s, etc. These cannot be accomplished by human beings. These were possible only due to Perumal’s avesha avatara – by Perumal making his unique prowess enter into a being and through that being carries out such acts. This is avesha avatara.