The word atma technically means ‘the Divinity’. So, in the Upnishads, except for a few places, the word atma has been generally used for God, the absolute Divinity, like how Brihadaranyak Upnishad says, “The supreme Divinity (God) should be desired by a soul to be visualized.” Aitreya Upnishad says, “The supreme Divinity (God) existed before the creation of this universe.”
The word brahm means the absolute Divinity Who is absolutely great and makes a soul great like Himself after God realization.
In the Upnishads the term brahm mostly refers to the personal form of God and occasionally to the impersonal (nirakar) aspect of God, just like the verse 7 in the Mandukyopnishad. The reason is that the nirakar aspect of God or nirakar brahm is formless and actionless and so it cannot even Grace the souls or become the creator of the universe or do any other thing of any kind. It is only the ‘purush,’ the personal form of God, Who does all those things. The Upnishads describe the Gracious kindness of God awarding liberation and His abode to the souls, and the creation of the universe etc. This is the work of the personal God only, that’s why there is very little description of the nirakar (actionless) brahm in them.
The most important thing is that nirakar brahm, being an existence of absolutely dormant virtues (avyakt shaktik), can never even manifest its Blissfulness. It is like the subtle dormant state of the beauty of a flower that dormantly exists in its seed that has not even taken the shape of a plant. So, wherever the Upnishads talk about the Divine knowledge or Bliss (chidanand) of brahm, they only refer to the personal form of God and not the nirakar brahm.
The Upnishads mostly use pronouns when referring to God, like, sah (He), ishah (controller God), purushah (personal God), and tasya (His) etc. However, there are a number of Upnishads like Tripadvibhushit Maha Narayanopnishad, Gopal Tapiniyopnishad, Krishnopnishad etc., which directly relate to the personal form of God and they clearly indicate that nirakar brahm is established in the personal form of God. So, personal form is the main form of God.
There is one more point that sometimes confuses the intellectuals. The Upnishads sometimes tell that the one who receives liberation becomes Narain or the one who receives liberation becomes brahm. That’s true, but the Upnishad further says that no one could be absolutely equal to God.
This situation is clarified by the producer of the Vedas, Bhagwan Ved Vyas himself. He says in the Brahm Sutra that the synonymity of a liberated soul does not synonymize him with the functions of God, like the creation, protection and destruction of the universe, or His absolute omnipresence etc. It only relates with the Blissful synonymity of the form of God he has attained.
It means that, upon God realization, the worshipper of the nirakar brahm enters the absolutely dormant state of the Divinity called kaivalya moksh and stays there forever in a kind of totally passed out state, because the nirakar brahm itself is an actionless dormant Divinity. The worshipper of God Vishnu, upon God realization, experiences the same kind and the amount of the Divine Bliss which God Vishnu Himself experiences in His abode, and so do the worshippers of Bhagwan Ram and Krishn. Isn’t it the incomparable unlimited loving Grace of God, Who awards His limitless personal Love and Bliss to a maya-inflicted soul who has committed uncountable transgressions and has accumulated uncountable sins in past unlimited lifetimes? Yet, the souls are so gross-headed that, ignoring His unlimited love, Grace and kindness, they remain engrossed in their material activities and lose the golden opportunity of having a human life which is the only hope of receiving His Grace and becoming His loving one forever.