Difference between Buddhi, Mann and Aatma
To understand the answer of the question a deep study of Rig Ved mandal 10 sukta 129 is essential. But is short one should understand about alive and non-alive matters. There are three matters in the universe. Almighty God and souls are alive. And prakriti is non-alive. It is stated in the said Rig Veda mantra 1 that when the previous universe had been destroyed and new one did not create then there was nothing to see. God, souls and prakriti was there, but in unseen stage. The sun, moon, sky, air, water, life, bodies of human beings, animals or birds, i.e., whole universe, was not there. Because the same had been destroyed which is called pralaya. Destruction means the whole articles of the universe were merged in prakriti. Prakriti has three qualities (gunas), raj, tam and satv guna. When these three qualities does not work then this stage is called prakriti.
So after final destruction (pralaya) God starts creation from prakriti i.e., the power of God works in prakriti and the whole world is created. The first creation comes out in the shape of MEHAT i.e., Buddhi. Then from Buddhi Ahankar and from Ahankar mann and chitta. From chitta panch tan matra and then panch mahabhoot i.e., prithvi (earth), Vaayu (air), jal (water), agni (fire), and akash (space) and from these five mahabhoots sun, moon, human bodies and other bodies etc., etc., etc., i.e., whole articles of world. Because prakriti is non-alive so the whole articles of the world is also non-alive. The bodies of man and woman and others were like statue because it is unsexual creation then the alive soul enters the body according to previous karmas (i.e., in the body of man, woman or animal or birds under the unchanged system of God).
We are soul and not body. Souls are immortal whereas all bodies are destroyed. Soul is atma. So this is the difference. But other differences are also there being several qualities of souls. When we sit in car and we drive the car and the car goes to our destination similarly we (soul) reside in the body and do every deed with the help of mann, Buddhi i.e., whole body. If the soul has to see then it will see through eye not himself, similarly to listen, to taste etc. So when soul has to think over any subject then soul takes help of Buddhi and mann.. because alone soul can do nothing. So it is a difference of thought of soul (atma), mann and Buddhi. But this is not an easy task to understand this philosophy due to lack of preach of Vedas/Shastras from a learned spiritual master.