Answer might depend on the school of vedAnta. That is fine. I want to know the position of different schools.
According to Chapter 15 of the Gita, a scripture accepted by all the schools of the Vedanta,
15.7 It is verily a part of Mine which, becoming the eternal individual soul [jivAtmA] in the region of living beings, draws (to itself) the organs which have the mind as their sixth, and which abide in Nature.
15.8 When the master leaves it and even when he assumes a body, he departs taking these, as wind (carries away) odours from their receptacles.
The above two slokas seem to describe the jivAtmA as a part of the ParamAtmA.
ParamAtmA on the other hand is described by
15.17 But different is the supreme Person who is spoken of as the transcendental Self (ParamAtmA), who, permeating the three worlds, upholds (them), and is the imperisahble God.
The AntaryAmi is the ParatmAtmA, about Whom Sri Krishna says:
18.61 O Arjuna, the Lord resides in the region of the heart of all creatures, revolving through Maya all the creatures (as though) mounted on a machine!
In the Mundakopanishad, these two has been referred to as the two good-winged birds and as per Advaita-vAda, there is no difference between the kivAtmA at the ParamArthika level.
A repesentation that explicitly mentions the word antarAtmA is found in the Kathopanishad:
Agnir yathA eko bhuvanam pravistah rupam rupam pratirupo bhabhuva/ ekas tatha sarvabhuta-antarAtmA rupam rupam pratirupo vahish cha, etc (As the same Fire appearing on the earth is seen in many forms according to the forms of the things it burns, the same AntaraAtman of all beings is seen in many forms and also present beyond these).
Here the Sarvabhuta-AntarAtma is One, though He appears differenty in each jiva.So here also there is no difference from the pAramArthika viewpoint, though apparently we see many.
Again Kathopanishad says
angusthamatrah puroshah antarAtmA sadA janAnAm hridaye sannivisthah. tam svAt sharirAt pravrihen..
meaning that AntarAtmA taking the size of a mere thumb resides in the hearts of all.His identity has to be separated from the body. This shows the path of illumination and so the word antarAtmA means paramAtmA or Ishvara, whom Sri Krishna referred to as the One residing in the heart.So antarAtmA and antaryAmi means the same Ishvara.