These clarifications are from Yogananda Maharaj and some from personal experience. There are three worlds. Gross physical world, the subtle world and the causal or karana world. The three forces, a sort of autonomic intelligence, hidden from the human eye are Virata, Hiranyagarbha and Ishwara respectively.
To give an eg. the function of Virata is to control the gross physical universe, all the physical properties of the universe including circling of planets around the star, mother nature in the world, gravity etc.
On an individual level, the three governing forces for the gross physical body, sukshma body and the causal body are called Vishwa, Tejas and Pragna. For eg. we do not have to tell the cells in the body to replicate or repair etc, it is done automatically. Scientists call it genetics but the Yogi refers the governing intelligence to Vishwa because there is a little more than just genetics to it.
Collectively these 6 forces are hidden forces. In the Mahabharata, there is the story of Ganga throwing her 7 children into the river. 6 of these “children” are the intelligent forces governing the individual and the gross 3 universes. They remain hidden / submerged in the flow of Ganga. The sevent child that remains hidden is called “abhasa chaitanya”, meaning although the entire universe it God, the universe remains as a reflection of God, not directly representing God. The eight child, Bhisma is the universal ego governing all three worlds.
One more aspect of clarification. Ishwara – intelligent force governing the causal world lives in Anahata Chakra. Thus, when the anahata chakra is pointing downwards, we call it Jeeva Kruta Maya. This has been described in great detail by Gurudev in Muktashastra. With constant practice, if we continually destroy the Jeeva Kruta Maya, then Ishwara or the upturned Anahata chakra which now reflects Ishwara is able to make all the necessary changes in the causal world and then subsequently in the gross world also. Gurudev has given many examples of this in Muktashastra. For eg. if we are meditating on this chakra, and all of a sudden we have the thought of collecting money from our debtor, the disciple says, “No, this is not my job, let Ishwara do it if he likes” Thus destroying the Jeeva kruta maya, Ishwara now takes over and the job is done without us moving from our meditation.
In Mahayoga vigyana and other Yogic text books, they have described Ishwara at Anahata chakra. I hope this explanation helps clarify the meaning and difference between Parmatma and Ishwara.
Bhavin